Meanwhile, wash and dry the fresh produce. Peel the carrots; halve lengthwise, then thinly slice crosswise. Halve, peel, and medium dice the onion(s). Halve the lemon(s) crosswise; squeeze the juice into a bowl, straining out the seeds. In the same pot, heat a drizzle of olive oil on medium-high until hot. Add the sliced carrots and diced onion(s); season with salt and pepper. Cook, stirring occasionally, 4 to 6 minutes, or until slightly softened. Add as much of the red pepper flakes as you’d like, depending on how spicy you’d like the dish to be. Cook, stirring occasionally, 30 seconds to 1 minute, or until combined. Add the broth (carefully, as the liquid may splatter), lemon juice, and reserved pasta cooking water. Simmer 2 to 3 minutes, or until heated through and the vegetables are softened. Add the spinach and cooked pasta; season with salt and pepper. Cook, stirring occasionally, 30 seconds to 1 minute, or until the spinach is wilted. Turn off the heat. Serve the soup topped with the pesto and parmesan. Enjoy!