Chop onion, carrot, shimeji mushrooms, and garlic. Remove the core of garlic before mincing.

Heat 1 tbsp olive oil in a pan over low heat, add garlic, and sauté until fragrant. Add ground meat and cook until browned. Add onion, carrot, and mushrooms, and sauté until onion softens.

Add canned tomatoes, water, ketchup, and red miso. Bring to a boil, cover, and simmer for 5–7 minutes on low heat. Uncover and cook for an additional 3 minutes on medium heat. Season with salt and pepper.

In a saucepan, heat 3 tbsp olive oil over medium-low heat. Add flour and stir until smooth. Gradually add soy milk while stirring until thickened. Mix in white miso until smooth.

Grease a baking dish with olive oil. Spread half of the soy milk cream sauce, layer 3 lasagna sheets, and add 1/3 of the meat sauce. Repeat layers twice, finishing with the remaining meat sauce. Top with pizza cheese and torn mozzarella cheese.