Pierce squash in several places with a sharp knife. Set squash in a microwave oven and cook at full power (100%) until soft when pressed, 10 to 12 minutes; turn squash over after 5 minutes.
Meanwhile, rinse, stem, and seed bell peppers. Peel carrots. Cut bell peppers and carrots into matchstick-size slivers.
When squash is tender, cut open and scoop out and discard seeds. Scoop out tender squash strands and reserve.
Set a 10- to 12-inch nonstick frying pan over high heat. Add bell peppers and carrots. Stir often until carrots are tender-crisp, 5 to 7 minutes.
Add broth, basil, pepper, and squash strands. Stir until squash is hot. Add salt to taste.
Pour vegetables into a dish. Sprinkle with cheese.