Heat the olive oil in a large skillet or pot over medium-high heat. Add the onion and saute for 4 to 6 minutes, or until soft. Add the garlic and mushrooms, stirring to combine.
Let the mushrooms cook for 4 to 5 minutes, or until they release liquid and start to brown.
Add the tomato paste, balsamic, basil, and red chili flakes, cooking for 1 minute.
Add the crushed tomatoes, vegetable broth, and lentils. Bring to a boil. Cover, and reduce heat to simmer for 30 minutes, stirring occasionally, until the lentils are tender and have begun to break down. Add the sugar, and season to taste.
Serve with pasta, and optional parmesan cheese and basil.
Store leftover sauce in the fridge for up to 4 days, or up to 3 months in the freezer.