Bring a large pot of water to boil for the green beans and pasta.
Preheat the oven to 350 degrees . Spread the nuts on a rimmed baking sheet and bake until toasted, about 6 minutes. Let cool; place in a food processor. Add the basil, parsley, mint, chile, garlic, lemon juice, and lemon and orange zest; season with salt and pepper. Pulse into a thick pesto, then gradually stream in EVOO until the pesto becomes a little creamy. Transfer to a large serving bowl; stir in the cheese.
Salt the boiling water. Add the green beans and cook until crisp-tender, 2 to 3 minutes. Using a strainer or large slotted spoon, scoop out the beans and transfer to a large bowl of ice water. When cold, drain and dry well. Add the beans to the pesto. Add the pasta to the boiling water; cook to al dente. Drain the pasta and toss with the pesto and beans; season. Serve at room temperature or cold, adding a drizzle of EVOO if the pasta seems dry.