Wash and dry all produce. Bring a large pot of salted water to a boil. Cut any large broccoli florets into bite-size pieces. Trim, then thinly slice scallions, separating greens and whites. Mince garlic.

Once water boils, add tagliatelle to pot. Cook 6 minutes, then add broccoli. Continue to cook until noodles are al dente and broccoli is just barely tender, about 2 minutes. Scoop out and reserve 1 cup cooking water, then drain.

Return empty pot to stove over medium heat. Add a large drizzle of olive oil, then stir in scallion whites, garlic, and Tuscan heat spice. Cook until fragrant, about 30 seconds, then pour in 3/4 cup reserved cooking water. Add cream cheese, stirring until well combined. Remove pot from heat and set aside for 1 minute to cool.

Once mixture in pot has cooled slightly, add yogurt, Italian cheese, half the Parmesan, 2 TBSP butter, and a few pinches of salt and pepper and stir until smooth.

Add tagliatelle and broccoli to pot with sauce and stir until well combined. If sauce seems thick, add more of the reserved cooking water until everything is covered in a loose but creamy coating. Season with salt and pepper.

Divide pasta between plates or bowls. Sprinkle with scallion greens and remaining Parmesan and serve.