Adjust rack to top position (top and middle positions for 4 servings) and preheat oven to 425 degrees. Bring a large pot of salted water to a boil. Wash and dry produce. Cut broccoli florets into bite-size pieces, if necessary.

Toss broccoli on one side of a baking sheet with a drizzle of olive oil; season with salt and pepper. Place bacon on empty side of same sheet. (For 4 servings, divide between 2 baking sheets; roast bacon on top rack and broccoli on middle rack.) Roast on top rack until broccoli is tender and bacon is crispy, 15-20 minutes. (TIP: If bacon is done before broccoli, remove from sheet and continue roasting broccoli.) Once bacon is cool enough to handle, chop into bite-size pieces.

Meanwhile, add spaghetti to pot of boiling water. Cook until al dente, 9-11 minutes. Reserve 1½ cups pasta cooking water (2 cups for 4 servings), then drain.

Once bacon and broccoli are done, heat pot used for pasta over medium heat. Add cheese roux and 1 cup reserved pasta cooking water (1½ cups for 4 servings); whisk to combine. Cook, whisking, until slightly thickened, 2-3 minutes. Lower heat to medium low and whisk in cream cheese to combine.

Add spaghetti, garlic herb butter, and half the Parmesan (you’ll use the rest later) to pot with sauce. Cook, tossing, until butter has melted and mixture is coated in a creamy sauce, 1-2 minutes. (TIP: If necessary, stir in more reserved pasta cooking water a splash at a time.) Taste and season with salt and pepper.

Stir bacon and broccoli into pasta. Divide between plates and top with remaining Parmesan.