Put a large pot of salted water on to boil for the spaghetti.
Fry the bacon until crisp in a large skillet, transfer to a paper towel-lined plate and set aside. Pour the excess fat from the pan, but don't wipe it out.
Add the olive oil to the pan and heat over medium heat. Add the onion, season with salt and pepper and sauté until soft and translucent, 4 to 5 minutes. Add the garlic and continue cooking about 2 minutes longer.
Stir in the chicken broth and thyme leaves and return the bacon to the pan. Continue cooking, stirring frequently, until the liquid is somewhat reduced, 3 to 4 minutes longer. Remove from the heat.
Cook and drain the pasta according to package directions.
Add the spaghetti to the onion mixture, drizzle with cream and toss until well combined. Adjust the seasoning as needed.
Plate individual servings and top with grated Parmigiana-Reggiano cheese. Serve with a salad.