Bring a large pot of salted water to a boil over high heat. Drop the pasta into the boiling water and cook to al dente
according to package directions.
While the pasta is cooking, place a medium pot over medium heat with the olive oil
. Add the bacon to the pot and cook, stirring occasionally, until golden brown and crispy, 5 to 6 minutes. Remove the bacon from the pot and reserve on a paper-towel-lined plate. Pour the residual grease
out of the pot, reserving about 1 tablespoon.
Return the pot to medium heat and add the garlic; cook until aromatic
but not golden, about 30 seconds. Add the flour to the pot and continue cooking for 1 minute. Add the milk
and mustard to the pot and bring the liquid up to a bubble; cook, whisking frequently, until thickened, about 1 minute. Add the squash to the pot and return to a bubble. Remove the pot from the heat, whisk
in the cheese, and season the sauce
with salt and pepper; reserve warm.
When the pasta has 3 minutes of cooking time left, drop the broccoli into the boiling water. Drain
the cooked pasta
and broccoli and combine with the cheese
with the reserved crispy bacon and serve.