Heat a large pot of water for pasta to a rolling boil, then salt liberally and drop in spaghetti to cook to al dente.
While the water comes to a boil and pasta cooks, place a large skillet over medium heat with 1/4 cup EVOO, four turns of the pan. When the EVOO is hot, add the garlic, shallots, carrots and zucchini. Season the vegetables with salt and pepper and cook for 10 minutes. Add the zest and juice of the orange and lemon to the pan and heat through. Add the butter and melt into the sauce, then turn off heat.
Drain the spaghetti and add to the skillet. Add the thyme, parsley and mint to the pasta and toss the spaghetti to combine with the veggies and absorb the sauce, 1 minute.
Serve pasta in shallow bowls with shredded radicchio on top as a spicy garnish.