Preheat oven to 400 degrees.
On a lightly floured surface, roll out the single sheet of puff pastry to a square. Cut into quarters, and lightly score the edges about an inch or so apart.
Place the puff pastry squares on a cookie sheet (parchment paper, non-stick spray, or a silicone mat will work on your cookie sheet). Bake for 15 minutes until the dough is golden.
Remove the squares from the oven and use a spoon to flatten the middle of the squares.
Add a quarter of the shredded cheese, and then top with bite-sized veggies of your choice. Anything will work here that you'd normally put in an omelet - tomatoes, onions, spinach, bell peppers, mushrooms. Leave enough space to crack an egg on top of the cheese and veggies so that the egg will stay on the center of the square. Sprinkle with thyme, salt, and pepper to taste. Repeat for all four.
Bake the egg-topped pastries in the oven again for about 20 minutes for a soft yolk.