Preheat your oven to 200°F to keep the cooked calamari warm. Char the lemon halves: place them cut-side down in a dry skillet over medium-high heat (or on a grill) and cook until browned, about 2–3 minutes per side. Set charred lemon aside.

Make the marinara: heat 1 teaspoon olive oil in a medium saucepan over medium heat. Add the diced shallot and minced garlic and cook, stirring occasionally, until softened, 2 to 3 minutes.

Add the 14-ounce can San Marzano crushed tomatoes, the grated small carrot, and 1 teaspoon Italian seasoning to the saucepan. Bring the sauce to a simmer, then reduce the heat to medium-low and simmer, stirring occasionally, until slightly reduced, 5 to 7 minutes.

Stir in 1/2 teaspoon kosher salt. Taste and, if desired, make only minor adjustments using the listed seasonings. Cover the pot to stop further reduction and keep the sauce on the lowest heat setting while you fry the calamari.

Prepare the dredging station: in a medium bowl, beat the 2 large eggs. In a large bowl, combine 1 1/2 cups all-purpose flour, 1/4 cup corn meal, 2 teaspoons Italian seasonings, 1 teaspoon kosher salt, and 3/4 teaspoon crushed red pepper.

Pour about 3 inches of vegetable oil into a medium pot and heat to 325°F. Use a thermometer so the oil stays near 325°F during frying.

Working in batches (do not overcrowd), transfer a portion of the calamari and tentacles to the beaten eggs and toss to coat.

Transfer the egg-coated calamari, a few pieces at a time, into the flour mixture. Toss or gently shake so each piece is thoroughly coated, then shake off excess flour.

Using a fork, slotted spoon, or tongs, carefully lower the coated calamari into the hot oil. Fry until light golden brown, about 1 to 2 minutes. Do not overcook — the pieces should be lightly browned.

Transfer the fried calamari to a paper-towel-lined tray to drain. Place the drained calamari on a baking sheet and keep in the 200°F oven while you fry the remaining batches. Maintain the oil temperature at about 325°F between batches.

After all calamari is fried and while the oil is still hot, add the 3–4 sprigs of Italian parsley to the oil and fry for about 30 seconds to 1 minute, until crisp. Remove and drain on paper towels.

Arrange the fried calamari and fried parsley on a serving plate. Spoon warm marinara sauce from the saucepan onto the plate or serve it alongside. Garnish with the charred lemon halves and serve immediately.