Heat a deep medium skillet over medium heat and add a splash of extra virgin olive oil.
Add the finely chopped garlic and sauté until golden and fragrant, about 30–60 seconds.
Add the ground turkey and cook, breaking it up with a spoon, until it changes color and is mostly cooked through.
Stir in the diced fresh tomatoes and 1/4 cup water, then simmer the mixture for about 15 minutes to combine flavors.
Season the sauce with dried oregano, salt, and black pepper; taste and adjust seasoning as needed.
Add the lasagna noodles, tearing them if necessary to fit and distribute evenly, and press them down into the sauce so they are submerged.
Reduce heat to low, cover the skillet, and simmer for about 10 minutes or until the noodles are tender and cooked through.
Turn off the heat, sprinkle the grated Parmesan and diced mozzarella over the top, then cover again and let sit until the cheeses melt, a few minutes.
Drizzle with a little extra virgin olive oil, garnish with finely chopped parsley, and serve.