Heat the oil in a Dutch oven or large pot over medium heat until shimmering. Add the onion and cook until softened, about 3 minutes. Add the garlic, oregano, salt, red pepper flakes, and several grinds black pepper and cook, stirring, until fragrant, about 1 minute. Stir in the tomato paste and cook until darkened in color, about 2 minutes.
Add the broth, marinara sauce, and beans and bring to a boil over medium-high heat.
Break the lasagna noodles in half crosswise, then in half crosswise again, creating four (2 1/2 inch) pieces from each noodle.
When the soup is boiling, add the noodles and reduce the heat to medium-low. Cook, stirring often to prevent the noodles from sticking to one another or the bottom of the pot, until very al dente (they'll continue to cook off the heat), 6 to 8 minutes. Remove from the heat and stir in the pesto.
Stir together the whipped cottage cheese and the Parmesan. Dollop onto individual servings of soup along with a drizzle of pesto. Garnish with fresh basil leaves.
