Preheat grill pan on stovetop.
Brush both sides of polenta slices very lightly with oil and place on grill pan to toast (approximately 3 minutes on each side).
Preheat broiler in oven to medium heat.
Meanwhile, melt butter with remaining two tablespoons of oil in a large, deep skillet over medium-high heat.
Add mushrooms and cook, stirring often, until tender and browned, (about 12 minutes).
Add shallots, vinegar, salt, black pepper, and red pepper and cook, stirring, until tender, (about 5 minutes). Stir in parsley.
Divide mushroom mixture between each piece of grilled polenta. Top with cheese and place under broiler until cheese is melted, (about 5 minutes).
Warm the sundried tomato pesto sauce and smear on the platter with the back of a spoon.
Arrange polenta bites on top of the sauce and serve.