I will echo the Bondo route that others suggested. The big box hardware stores sell quart cans of general purpose Bondo in the paint aisle.
Cut out the vaneer over the bad area with a razor blade or box cutter.
Sand with 80 or 120 grit to remove any loose bits of the board. The particle board will crumble a little, but it will be fine. Just dont go overboard. Vacuum it to remove most dust.
Using a flexible putty knife, get one to two globs of Bondo on a clean piece of cardboard. Don't do too much as you will have about 5 minutes of working time once the hardener is added. Follow the instructions on how much hardener to add, you wont need much. Fold the hardener into the Bondo with the putty knife until it is a uniform color.
Spread the bondo over the area you cut out. Try to get it smooth, but dont overwork it. It doesn't have to be perfect.
Using 60 or 80 grit paper, sand it as it starts to dry. If it is gumming up the paper, it is still too wet to sand, give it another minute or two and try again. You are shaping it with this step. If you let it completely dry, it is hard as a rock and more difficult to sand.
Once it is in a good shape, switch to the next step up for sanding and repeat (60 to 80 to 120 to 180 to 220). Do not skip gits or you will just make work for yourself. You can probably stop at 180, but since it is next to vaneer, i'd go to 220. Again, if it is gumming the paper, wait a few minutes. Once you are at 220, use it to sand the entire cabinet to rough up the surface and accept primer better.
Once sanded, wipe the entire cabinet down with a tac cloth. I also recommend wiping the cabinets with a wax and greese remover so everything will stick better.
Now it is time for primer and paint. For a smooth finish, use a good quality foam mini-roller and foam brush for tighter areas.
Prime the cabinet using any water-based primer; killz is pretty good. They make an oil based that would be better, but will smell up your whole house, so I don't recommend it unless you have excellent ventilation.
Lightly sand the peimer once it is fully dried with 220. If any spot is too light, do a second coat. Wipe up the dust.
Paint with an alkyd paint. Do at least 2 coats.
Not necessary, but if you want extra protection, you could use a foam brush (not a roller here) and do 3 to 4 coats of a water-based polyurethane on top of the paint. It might be overkill for what you want though.
This might seem like a lot, but you will have a great finish when done. Also, fair warning, Bondo has a strong smell. Open a window.
I get why people are upset by the headline. It is written to provoke anger. Unfortunately, anger at the wrong issue.
I understand the argument that a large company can absorb the cost of workers they don't currently. Though it's unrealistic to expect them too.
I lived in the Quad Cities for a number of years. A large majority of people I know, both family and friends, worked for either Deere or Case IH - until they closed the plant in East Moline.
Layoffs are a yearly thing. Deere, Case, Caterpillar, they all hire a bunch of people in the beginning of the year and lay them off towards the end. It's typically around August or September, and they announce it in July. Everyone in the Quad Cities knows it. It is expected. Sometime early next year, they are going to hire these jobs back. The people who take these jobs go into it knowing this is going to happen.
It can suck being let go and some people might struggle with it. Those who are used to this cycle treat it as a well-paying seasonal job. Many already have something else lined up. This is only a single, anecdotal, data point, so take it with a grain of salt... one of my uncles works for Deere and is a bus driver for one of the school districts. He knows Deere is going to let him go by fall so he has the driving job for the rest of the year. In spring, he will go back to Deere.
Perspective is also important. Deere has somewhere between 80k and 85k employees. They are laying off < 1000 based on this story. That's the equivalent of a small, 80 person company hiring 1 person to get through the holiday season, then laying them off in January. Next year, they will do it again.
Headlines like this are nothing more than a distraction from real issues. For example, why does any company have multi-billions of dollars in profit to begin with? It just means they are charging more than they need to. The farmers who buy Deere equipment then have to charge more for their produce. Which means the stores have to charge more. Which means we pay more for our food. Deere's profits are leading to higher food prices for everyone. To me, that is more of an issue than 1/80th of their workforce being in a hire/layoff cycle.