Heat oil in a medium saucepan over medium-high heat.
Add garlic, thyme and crushed red pepper and cook, stirring, for 1 minute.
Add broth, penne, cauliflower and squash. Bring to a boil over high heat.
Reduce heat to a lively simmer and cook, uncovered, until the pasta is tender and the liquid is thickened and greatly reduced, 10 to 15 minutes. Remove from heat, stir in pepper and let stand for 5 minutes.
Serve topped with cheese.