Step 1Make the spicy marinara: In a medium saucepan, heat olive oil over medium-low heat. Add garlic and red pepper flakes and cook, stirring, until garlic is soft, 3 to 4 minutes. Add tomato paste and cook, stirring, 1 minute. Add crushed tomatoes, oregano, and basil (if using). Bring to a simmer and cook 5 minutes; season to taste with salt and pepper. For a chunkier sauce, leave as is. For a smoother sauce, let cool slightly and transfer to a blender to puree.
Step 2Make the calamari: Using your hands, pull apart mushrooms so they are separated into “petals.” In a medium bowl, combine flour, panko, salt, pepper, garlic powder, and paprika. In another medium bowl, whisk nondairy milk and yogurt to combine.
Step 3Fit a deep skillet or pot with a deep fry thermometer and add canola oil to a depth of 3 inches. Place over medium high until thermometer registers 375°F.
Step 4Working in batches, dunk mushroom pieces in milk mixture, shaking off excess. Dredge in flour mixture, making sure pieces are evenly coated. Transfer to a parchment-lined baking sheet or plate and repeat until all pieces are coated.
Step 5Fry mushrooms in batches, turning occasionally, until golden brown, 3 to 4 minutes. Transfer to a paper towel-lined plate to drain and season with salt. Serve with marinara and lemon wedges.