Put the cashews, soy milk, broth, and nutritional yeast in a blender or food processor and process until completely smooth (which may take a few minutes), stopping occasionally to scrape down the sides of the blender jar.
Heat the olive oil in a medium pot over medium heat. Add the onion and sauté until tender and translucent, about 8 minutes. Add the garlic and sauté until very fragrant, 2 or 3 minutes.
Stir in the crushed tomatoes, tomato paste, oregano, thyme, pepper flakes, and the blended cashew mixture. Decrease the heat to maintain a simmer.
Cook, stirring occasionally, until heated through and thickening slightly.
Using an immersion blender (or using a regular blender and working in batches), blend until smooth and creamy, then season with salt to taste.
Just before serving, stir in the basil.