Preheat the oven to 425 F. Line a baking sheet with parchment paper. Cut peppers in thirds, removing stems and seeds. Half tomatoes. Half onions, removing outer, papery layers. Remove tops and bottoms of garlic heads to break them apart into chunks (don't peel completely - groups of cloves can still be stuck together). Add these veggies to the baking sheet with a drizzle of oil and sprinkle of salt.
Bake veggies for about 45 minutes - stirring occasionally. While this is happening, slice the summer squash and add them to the baking sheet when there are 15 minutes left. Veggies should be tender and pepper skins beginning to char.
Remove from oven. You can use a glove for some protection from the heat, or allow to cool for several minutes. Place veggies into a saucepan, squeezing the garlic cloves out and discarding peels. (At this stage, you could allow the veggies to cool for longer and remove peels from the tomatoes and peppers as well, but that's not my style). In a separate pot, bring water and salt to a boil.
Add pasta to boiling water, and set a timer for package direction duration.
Back to our veggies! Before placing onto a heated burner, carefully use an immersion blender to blend veggies into a homogeneous sauce. If moisture is needed, you can add 1/4 cup of the pasta water at a time until reaching desired consistency. Then, place on a burner at low heat to simmer.
Stir your cheese and maple syrup into the sauce - trust me on the maple syrup. It adds body and takes the edge off the acidity of fresh tomatoes. At this stage, continue to stir and taste test, adding salt or more maple if salty or sweetness is needed. If you want your sauce more tart, try adding a few fresh tomatoes. If it's spice you're looking for, chili flakes would make a great addition.
When the pasta is done, drain and add to the sauce pot. Turn off heat and stir to combine.
Stack basil leaves on top of each other, fold them in half, and then use a sharp knife to cut thin ribbons. Serve your pasta, stirring in basil and adding a whole leaf for garnish.