Bring a large pot of water to a boil. Add salt, then the pasta, and cook until al dente, about 9 minutes; drain. (Heads up: Reserve a ladle of the cooking water before you drain the pasta.)
While the pasta cooks, halve the zucchini lengthwise, then thinly slice into half-moons. Peel the carrot; then, holding the carrot at the root end, use the peeler to thinly slice lengthwise. Place the carrot strips on the cutting board and chop into small pieces-like carrot confetti!
Heat the EVOO, 2 turns of the pan, in a large, deep skillet over medium-high heat. Add the zucchini, carrot confetti and mushrooms to the skillet. Cook the vegetables for 3 minutes, tossing once, then add the onion and garlic to the pan. Season the vegetables with salt and pepper and toss with tongs. When the onions are tender, about 5 minutes more, add the peas and roasted red pepper and toss to heat through. Transfer the veggies to a large dish.
Return the skillet to the stove over medium-low heat and add the butter. When the butter melts, add the flour and whisk for a minute or so, then whisk in the broth and milk. Bring to a bubble and thicken the sauce by letting it reduce for 3 to 5 minutes. Season with salt, pepper and the nutmeg. Slide the vegetables into the sauce.
Return the reserved ladle of pasta water to the pasta pot and bring it to a boil. Turn off the heat, stir in the ricotta, then add the grated cheese. Add the pasta to the cheeses. Top the pasta with the veggies and sauce, then toss to combine. Tear or shred the basil and toss into the pasta. Adjust the seasonings. Pass around the extra grated cheese at the table.