Place a large skillet over medium-high heat. Pour in 2 tablespoons oil, add onion and saute for 4 to 5 minutes. Add garlic and continue to saute for an additional minute. Season with salt and pepper.
Add turkey, breaking up with a wooden spoon and brown for 3 to 4 minutes. Season with salt and pepper. Transfer turkey mixture to a mixing bowl and set aside.
Place skillet back stove and lower heat to medium. Add remaining tablespoon of oil and kale and saute for 3 to 4 minutes, until kale has just wilted. Season with salt and pepper and transfer to another mixing bowl.
Using the back of a wooden spoon, press kale and drain excess liquid from kale.
Place skillet over stove for a final time and lower heat to medium-low. Add butter and melt.
Sprinkle flour over butter and stir together with a wooden spoon for about 3 minutes to remove raw flavor of the flour.
Slowly add milk, while stirring, until all milk has been added. Continue to stir mixture together until completely smooth and mixture thickens enough to coat the back of a wooden spoon. Season with salt and pepper. Remove from heat and sprinkle Parmesan over mixture and stir together until smooth and creamy.
To assemble: Preheat oven to 375˚F.
Lightly grease 3 (6”) skillets with 1 tablespoon butter each. Pour a heaping spoonful of béchamel over each skillet and top each skillet with 2 pasta sheets, slightly overlapped.
Top pasta sheets with ¼ heaping cup of ground turkey, followed by a thin layer of kale. Pour about 3 tablespoons béchamel and sprinkle about 2 tablespoons shredded mozzarella over kale. Repeat with another layer of pasta sheets, turkey, kale, béchamel, and mozzarella. Top each skillet with 2 more pasta sheets remaining béchamel and shredded mozzarella. Finish each skillet with a vine of cherry tomatoes and place onto a large baking sheet.
Bake skillets for about 30 minutes or until bubbling and slightly browned on top. Remove from heat and allow lasagnas to cool for about 10 minutes before serving.