Heat a large nonstick skillet over medium-high heat.
Add oil; swirl to coat.
Add sausage; saut 3 minutes or until browned.
Add onions, thyme, and garlic; saut 5 minutes.
Remove from heat.
Bring milk to a simmer in a large saucepan. Reduce heat to medium-low. Stir in polenta and salt; simmer 7 minutes, stirring frequently with a whisk.
Remove from heat.
Add cheeses; stir until cheeses melt.
Place the polenta mixture in a large bowl; let stand 15 minutes, stirring occasionally. Stir in pepper sauce and eggs.
Add sausage mixture; stir well to combine.
Spread polenta mixture into a 2-quart glass or ceramic broiler-safe baking dish coated with cooking spray. Cool to room temperature. Cover surface with plastic wrap; refrigerate overnight.
Preheat oven to 42
Uncover dish.
Bake at 425 for 25 minutes or just until set.
Preheat broiler to high; remove dish while broiler preheats. Broil 2 minutes or until top is lightly browned.