Preheat the oven to 350F Season the ribs all over with salt and pepper.
Lightly coat the bottom of a heavy braising pot with oil. Heat to hot and then, working in batches, brown the ribs on all sides. Give them a few minutes per side to make sure they get nice and brown. Remove the ribs to a plate.
Add the onions and carrots to the pot and saute for a few minutes until they start to soften. Stir often, scraping up the browned bits from the bottom of the pan.
Add the flour and tomato paste and continue to cook and stir. It's ok if it starts to stick to the pan, but stir constantly for a minute or two and don't let it burn.
Add the wine to the pan and then the short ribs. Bring to a boil, scraping the bottom of the pan as it heats. Lower the heat and gently boil for about 15 minutes, or until the wine has reduced by about 1/3.
Add the herbs, garlic, and beef stock to the pot stir well. Bring up to a boil, then cover, and transfer the pot to the oven and cook for 2 1/2 to 3 hours. Tip: after about 30 minutes I check the pot, if it's gently simmering, great. But if it's rapidly boiling, turn down your heat to 325F.
Remove the ribs, carefully, from the pot and set on a plate. They should be falling off the bone and fork tender.
Strain the gravy and discard the solids.
Serve the ribs, 2 per serving, on top of hot polenta and ladle with gravy. Garnish with fresh thyme (or parsley.) Tip: the gravy should be thin, but if you'd like it thicker, just boil it down in a saucepan until it reaches your desired thickness.
To make polenta
Bring the water, milk, and salt to a boil in a saucepan. Slowly sprinkle in the polenta, whisking constantly.
Lower the heat and cook, stirring often, for about 15 minutes, or until thick. You can partially cover the pot to protect against eruptions!
Remove from the heat, add in the butter and cheese and stir until melted. Check the seasonings.