Add the olive oil to a medium pot over medium heat. Once it's hot, add the onions and garlic and cook until the onions are translucent, 3 to 4 minutes. Add the tomato paste and red pepper flakes and stir until the tomato paste is thoroughly incorporated. Add the crushed tomatoes to a food mill and process the tomatoes directly into the pot. Add the grated carrots and season with kosher salt. Reduce to low heat and simmer for 20 minutes. Adjust the seasoning as needed. Cover and put aside to keep warm.
Heat the canola oil in a large Dutch oven or large heavy-bottomed pot over medium-high heat to 350 degrees F. Line a sheet tray with paper towels.
Add the rice flour, semolina flour, pepper and 2 teaspoons kosher salt to a large shallow dish and mix until thoroughly combined. Working in 3 batches, toss the calamari, pickled pepper slices and rosemary sprigs in the seasoned flour, then scoop them out with a pasta spider and shake off the excess; transfer to the oil. Fry for 90 seconds, then remove to the paper towels and season with flaky sea salt. Repeat until all the calamari is cooked.
Serve with the lemon wedges and spicy marinara on the side.