Melt butter in a large skillet over medium heat. Add pasta then stir to coat in the melted butter. Cook the penne for 2 minutes, stirring occasionally and allowing it to toast and become light golden brown.
Add onion and cook until it is lightly browned, about 30 seconds.
Add chicken broth to the skillet then stir the mixture until it comes to a bubble. Immediately reduce the heat to low then cover. Simmer the pasta on low, covered, for 10 minutes.
Remove the lid, add the broccoli florets then stir to combine. Most of the liquid should be absorbed by the penne at this point, but there should be just enough liquid left to steam the broccoli. If the mixture is too dry, add 1-2 Tbsp of water. Cover the skillet and allow the broccoli to steam for 2 minutes.
Remove the lid, add Asiago and cheddar cheeses and stir until melted and fully incorporated into the mixture.
Remove the skillet from heat and test the penne for doneness. If the pasta is slightly undercooked, place the lid on the skillet and allow it to sit (off the heat) until it softens. If the mixture is too thick, add 1-2 Tbsp of milk to achieve the desired consistency.
Before serving, garnish with additional Asiago cheese. Enjoy!
Notes
If you’re lucky enough to have leftovers, this dish tastes even better on day two!