Remove the cream cheese from the fridge about 30 minutes before cooking so it softens, or microwave for about 30 seconds if needed.
Bring a large pot of salted water to a boil and cook the pasta until al dente according to package directions; reserve a splash of pasta cooking water, then drain.
While the pasta cooks, heat the butter in a large skillet over medium heat.
Add the softened cream cheese, Frank's RedHot sauce, chicken broth, and ranch seasoning to the skillet and stir until the cream cheese melts and forms a smooth sauce, 2–4 minutes; let it cook briefly to thicken.
Stir the shredded cheddar into the sauce until melted, then add the cooked chicken and warm through, taking care not to overcook.
If the sauce seems too thick, loosen it with a splash of the reserved pasta water.
Add the drained pasta to the skillet and toss to combine so the pasta is evenly coated with sauce; season with salt and pepper to taste.
Serve immediately, sprinkled with chopped scallions if desired.