Season the chicken with salt and pepper
Select the SAUTE setting and adjust to More for high heat.
Heat oil in the pot until it shimmers and then add the chicken thighs, skin-side down, and let them cook, undisturbed, until the skin is dark golden brown and most of the fat under the skin has rendered out, about 5 minutes. Don't overcrowd the chicken, you may need to work in batches.
Turn the thighs and cook until light golden brown on the other side, about 3 minutes.
Transfer the thighs to a plate and set aside.
Carefully pour off almost all the fat, leaving just enough to cover the bottom of the pressure cooker with a thick coat (about 1 tablespoon).
Add the carrots and let them cook, undisturbed, until they begin to brown, about 2 minutes.
Add the stock and scrape the bottom of the pan to release the browned bits.
Add the vinegar, honey, mustard, and thyme and stir to combine.
Return the chicken thighs, skin-side up to the pot.
Lock the lid into place and select MANUAL, or MEAT/STEW and adjust the pressure to High and the time to 10 minutes.
After cooking, naturally release the pressure for 5 minutes, then manually release any remaining pressure
Remove the chicken thighs from the pot and place them, skin-side up, on a rack set over a baking sheet.
Meanwhile, preheat your oven broiler to high.
Place the baking sheet and rack with the chicken thighs in the oven on the top or second rack (depending on the strength of your broiler).
Broil until browned, 3 to 5 minutes (keep an eye on them, don't let them burn!).
Meanwhile, select the SAUTE setting on high and let the sauce simmer for several minutes until it's somewhat thickened, about 3 minutes. .
To serve, ladle a spoonful of sauce onto each plate and top with a spoonful of carrots and a chicken thigh. Serve at once.