Bring a large pot of salted water to a rolling boil and add pasta. Cook according to package directions minus 2 minutes. During the last 3 minutes of pasta cooking time, add the broccoli florets directly to the same pot. The broccoli should turn bright emerald green and become fork-tender. Reserve 1 cup of the starchy pasta water before draining.

While the pasta finishes cooking, melt butter in a large skillet over medium heat until it starts to foam and smell nutty. Add minced garlic and sauté for about 30 seconds until fragrant but not browned.

Pour the heavy cream into the skillet and bring to a gentle simmer, stirring frequently. Add the softened cream cheese in small pieces, whisking until completely smooth and lump-free. The mixture should coat the back of a spoon and have a velvety consistency.

Add the drained pasta and broccoli to the creamy sauce, tossing gently to coat every piece. Gradually sprinkle in the Parmesan cheese while continuously stirring. If the sauce seems too thick, add reserved pasta water one tablespoon at a time until you achieve a glossy, coating consistency. Season with salt, pepper, and red pepper flakes, then finish with fresh lemon juice.