Place the chicken thighs in the bottom of the slow cooker. Add the sliced onion, red bell pepper, mushrooms, and minced garlic on top.
Pour the crushed tomatoes over the vegetables and chicken. Sprinkle the oregano, basil, salt, and black pepper across the surface. Stir lightly to distribute the seasonings.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours until the chicken is very tender.
About 30 minutes before serving, bring 3 cups of the chicken broth to a boil in a saucepan. Slowly whisk in the cornmeal.
Lower the heat and cook the polenta, stirring frequently, for about 20 minutes until it thickens. Add the remaining broth a little at a time if it becomes too stiff.
Remove the polenta from the heat and stir in the butter and Parmesan cheese until smooth. Taste and adjust salt if needed.
Spoon the polenta into bowls and top with the chicken and sauce. Scatter chopped parsley over each serving if using.