Preheat oven to 450 degrees F. On a rimmed baking sheet or oven-safe skillet, toss together tomatoes, sliced garlic, and 2 Tablespoons of the olive oil. Roast for 10 minutes, until the tomatoes are wrinkled and just beginning to burst. Remove from oven and set aside.

While the tomatoes roast, combine butter and remaining 2 Tablespoons olive oil in a large skillet over medium-high heat.

When the butter is melted, add gnocchi to the pan and stir to coat. Let the gnocchi cook for about 5 minutes without stirring, until they begin to brown and turn crispy on the bottom. At that point, stir the gnocchi and cook for another 2-3 minutes to lightly brown the other side. If at any point the pan is getting dry or the gnocchi are browning too quickly, reduce heat to medium and/or add an extra drizzle of olive oil.

Add the roasted tomatoes and garlic, slivered basil, pine nuts, and red pepper flakes to the skillet. Sample and season with salt and pepper to taste. Serve right away.