Heat a large nonstick skillet over medium high heat. Add oil; swirl to coat. Add the sausage; saute 3 minutes or until browned. Add the onions, thyme, and garlic; saute 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 the cheeses; stir until the cheeses melt. Place the polenta mixture in a large bowl; let stand 15 minutes, stirring occasionally. Stir in pepper sauce and eggs. Add the sausage mixture; stir well to combine,
Spread the mixture into a 2 quart glass or ceramic broiler-safe baking dish coated with cooking spray. At this point you can go ahead and bake it or cool to room temperature, cover, and refrigerate overnight.
Preheat the oven to 425 degrees. Uncover the dish. If it was refrigerated allow it to sit out while the oven preheats. Bake at 425 degrees for 25 minutes or just until set.
Preheat the broiler to high; remove the dish while the broiler preheats. Broil 2 minutes or until the top is lightly browned. Let it stand 5 minutes.