Fill a medium pot 3/4 of the way up with salted water; cover and heat to boiling on high. Once boiling, add the pasta. Cook, stirring occasionally, 8 to 10 minutes, or until tender. Turn off the heat. Reserving 3/4 cup of the pasta cooking water, drain thoroughly. Transfer the cooked pasta to a bowl; add a drizzle of olive oil and stir to coat. Rinse and wipe out the pot.

Meanwhile, wash and dry the fresh produce. Peel the carrots; halve lengthwise, then thinly slice crosswise. Halve, peel, and medium dice the onion. Halve the lemon 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; 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!