Preheat oven to 400˚F.
Sausage gravy filling: Place a large skillet over medium-high heat and brown/crumble sausage, about 4 minutes. Transfer sausage to a mixing bowl and set aside.
Drain grease from skillet, add butter and melt over medium heat.
Add potatoes and onion and sauté for 6 to 8 minutes or until potatoes turn tender and onions lightly caramelize. Season with salt and pepper.
Add garlic and sweet peppers and continue to sauté for 2 to 3 minutes. Stir in herbs. Sprinkle flour over mixture and stir together for about 2 to 3 minutes. Slowly stir milk into the mixture and continue to stir until gravy is smooth and mixture is thick enough to coat the back of a wooden spoon. Fold sausage back into the gravy mixture and adjust seasonings. Set aside and keep warm.
Puff pastry topping: Cut thawed puff pastry sheet down the middle, both vertically and horizontally, so you have 4 even rectangles. Using a 2 ½ inch circle cutter, cut a circle out of each piece of puff pastry. Place each rectangle, plus cut circle onto a parchment lined baking sheet and bake for about 10 minutes.
To assemble: Divide the filling mixture amongst 4, 6″ skillets. Remove par-baked puff pastry rectangles from the baking sheet and set each one over a gravy filled skillet and gently press. Crack an egg into the cut out circle of each pastry rectangle and place mini skillets onto the baking sheet (circles of puff pastry should still be on the tray).
Place baking sheet back into the oven and reduce temperature to 375˚F.
Bake pot pies for 15 to 20 minutes or until the puff pastry is golden brown and the egg whites have set, with the yolks still runny. Lightly season with salt and pepper, top with minced thyme and serve immediately.