• Heat a large heavy bottomed pot (I like using my enamelled cast iron pot for recipes like this) over medium-high heat and add the olive oil.
• Season the cubes of beef chuck with salt and pepper and brown them on all sides in the pot. You may have to do this in 2 batches to avoid overcrowding the pan. Don't worry about cooking the beef all the way through at this stage - just brown the outside.
• Remove the browned beef to a plate and add the onions, garlic, carrots and celery to the pot. Let the vegetables cook just until they've begun to soften.
• Add the mushrooms and cook for a few minutes more, stirring often.
• Add the beef back into the pot and sprinkle the flour over the beef, stirring everything together well until the flour disappears.
• Add the tomato paste and the red wine, stirring well until the wine begins to reduce.
• Stir in the beef stock and cover the pot, reducing the heat to low.
• Let cook on low for about one to two hours, stirring every 20 minutes or so (stir every 10-15 minutes for the first half hour).

For the polenta:

• Just before you're ready to serve, add the cornmeal, cream or milk, stock and salt to a large saucepan over medium high heat.
• Stir the mixture together with a whisk as it heats up and comes to a boil.
• Once it reaches a boil and thickens, remove it from the heat and add the parmesan (optional), stirring it in just until melted.
• Serve the polenta in bowls (just under 1 cup of cooked polenta per serving) and top it with the braised beef and some freshly chopped parsley (optional).