1.) Preheat the oven to 425 degrees F.
2.) On a rimmed baking sheet, toss together the brussels sprouts, olive oil, thyme, and a pinch each of salt and pepper. Lay the brussels sprouts cut side down on the baking sheet. Sprinkle the bacon around the sprouts. Roast the brussels sprouts until deeply browned and the bacon crisp, 20 to 25 minutes.
3.) Meanwhile, whisk together the eggs, parmesan, garlic, and salt and pepper in a bowl.
4.) Bring a large pot of salted water to a boil. Boil the pasta until al dente. Before draining, scoop out about 1 cup pasta water, then drain.
5.) Immediately add the hot pasta back to the pot. Add the egg cheese mixture, tossing quickly (to ensure the eggs do not scramble) until the eggs thicken and create a sauce. Thin the sauce with a bit of the reserved pasta water, until it reaches your desired consistency. Add the butter and gently toss to combine. Season with salt and pepper.
6.) Divide the pasta among plates and top with parmesan, brussels sprouts, and bacon. Drizzle a bit of olive oil over top. Enjoy!