Bring a large pot of water to a boil. Add pasta, cover and return to a boil. Reduce heat to a simmer and cook for 5 minutes; add edamame and cook for 4 minutes. Add peas, mushrooms broccoli and radishes and cook until vegetables are tender, about 1 more minute. Drain.
Meanwhile, in a blender, purée sauce ingredients until smooth, 1 to 2 minutes.
Return pasta mixture to pot and add tomatoes, shallots and pepper flakes. Stir in sauce, cheese and nuts. Heat on low and cook, stirring occasionally, until just warmed through. To serve, top with basil.
Tip: If you want to add a little variety, try serving half the recipe on eggplant rounds and the other half on Portobello mushroom caps. They both take the same amount of cooking time and offer a toothsome, meaty texture.