Place the basil, parsley, cheese, mint, pine nuts, thyme, garlic and lemon juice in a food processor and season with salt and pepper. Turn the processor on and add the EVOO in a slow stream, blending until a thick sauce forms. Transfer to a large bowl.
Bring a large pot of salted water to a boil. Add the pasta and cook for 6 minutes. Add the potatoes and cook for 1 more minute. Add the haricots verts and cook until the pasta is al dente, 2 to 3 more minutes. Reserve 1 cup of the cooking water and add it to the pesto. Drain the pasta, then add it to the bowl with the pesto and toss to coat.