Melt butter in a large heavy pot over medium heat. Add bacon and cook, stirring often, until fat is rendered and bacon is crisp, 7-10 minutes. Add leeks and season with salt and pepper.
Increase heat to medium-high and cook, stirring often, until leeks begin to brown, 5-8 minutes. Add broth and stir to remove browned bits from bottom of pan. Stir in cream and thyme. Bring to a boil, reduce heat, and simmer, stirring occasionally, until sauce is thickened and coats the back of a spoon, 5-8 minutes.
Meanwhile, cook pasta according to package directions. Drain, reserving 1 cup of the pasta cooking liquid.
Add cooked pasta, 3/4 cup Parmesan cheese, and 1/2 cup pasta cooking liquid to the cream sauce and stir to coat. Add more cooking liquid as needed, until sauce reaches desired consistency.
Season with salt and pepper, to taste. Before serving, garnish with additional Parmesan cheese and fresh parsley, if desired.