For the marinara sauce: In an 8-inch saucepan, add the olive oil along with the onion and turn the heat to medium. Add a small pinch of salt and saute until the onion softens and develops a bit of color, about 6 minutes. Add the garlic and cook for 1 minute more. Add the tomatoes along with the sugar and oregano, partially cover the saucepan with a lid, bring to a simmer and cook until the sauce reduces and deepens in color, about 20 minutes.
Remove the lid, add the basil, season with salt and pepper to taste and cook for 5 additional minutes.
For the pot roast with porcini mushrooms: Season the beef well with 1 tablespoon salt and 1 1/2 teaspoons pepper all over and allow it to rest at room temperature for 15 minutes. Bring 1 cup of water just up to a boil and transfer to a small bowl along with the porcini mushrooms. Set them aside to rehydrate for 6 minutes.
Heat a large Dutch oven over medium-high heat, add the canola oil and allow it to get hot. Add the beef and brown on all sides for 3 to 4 minutes per side, a total of 6 to 8 minutes. Remove the beef from the pan and reduce the heat to medium. Add the garlic, celery, carrots and onion along with a small pinch of salt and pepper and saute until the veggies develop some color and cook down a bit, about 7 minutes.
Add the beef back in along with the wine, beef stock, rosemary and 2 cups of the marinara sauce. Add the rehydrated porcini mushrooms along with the soaking liquid, making sure to avoid the last few tablespoons because there will be some grit at the bottom of the bowl. Bring to a boil and reduce the heat to medium low. Cover and let cook for about 3 1/2 hours, flipping the meat halfway through.
After 3 1/2 hours, add the pearl onions. Turn the heat back up to medium high and cook, uncovered, for 20 more minutes, flipping the meat over halfway through. Remove the roast and allow it to rest for a bit before shredding it into large chunks. Skim the fat from the sauce. After shredding the meat, stir it back into the sauce.
For the polenta: Meanwhile, in a large pot, bring the milk and 5 cups water to a gentle boil. Add the polenta along with a good amount of salt and pepper and cook, stirring constantly, for about 5 minutes.
Turn the heat down to low, partially cover the pot and allow the polenta to simmer for about 20 minutes, giving it a stir every 5 minutes; depending on the size of your polenta or cornmeal, it may take more or less cooking time to become creamy.
Turn the heat off, add the butter and cheese and stir until the butter and cheese melt. Top with a serving of the pot roast and sauce.
The polenta hardens as it sits.