Finely chop onion; slice garlic; drain and rinse beans.
Heat 3 tablespoons olive oil in a large saucepan over medium heat. When it shimmers, add onion and ¼ teaspoon salt. Cook until onion is softened and just beginning to brown, about 5 to 7 minutes.
Add garlic and cook until golden, about 2 minutes more.
Add tomatoes, their juices, and beans and bring mixture to a boil. Reduce heat to medium low and bring mixture to a simmer. Cook until sauce is slightly thickened, about 20 minutes.
Grate ½ cup parmesan cheese using a box grater.
Bring 4 cups stock, 2 cups water and ½ teaspoon salt to boil in heavy large saucepan.
Gradually whisk in 2 cups polenta; whisk constantly until mixture is smooth and begins to thicken.
Reduce heat to low and cook until tender and thickened but still creamy, stirring often, about 5-10 minutes more.
Turn off heat and stir in 2 tablespoons olive oil and ½ cup Parmesan cheese.
Spoon ¾ cup polenta into a bowl and top with 1 cup of sauce.
Serving Size 3/4 cups polenta, 1 cup sauce
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.