The bright hues of this "lasagna plaid" pasta come from vegetables, not dyes. The pasta can be found online.
Place tomatoes in a large mixing bowl. Combine oil, garlic, and red-pepper flakes in a small pan over medium heat. Cook until garlic is fragrant and oil starts to simmer. Pour over tomatoes; season with salt.
Bring a large pot of salted water to a boil and cook lasagna sheets until tender, 13 to 15 minutes; drain. Transfer sheets to the bowl with the tomatoes and stir to coat. Garnish with basil and cheese, and drizzle with olive oil.