Pat the frog legs dry and season them aggressively with salt and pepper. In a Dutch oven, heat 2 tablespoons of olive oil over high heat until smoking. Add the frog legs and sear until dark golden brown on all sides. Remove the frog legs to a plate lined with paper towels and set aside.
In the same pan, place the onion, carrot and celery and cook over high heat until the vegetables are browned and soft. Sprinkle the flour over the vegetables and cook, stirring for another 2 minutes. Add the white wine and stir with a wooden spoon to dislodge the browned bits at the bottom of the pan. Add the tomatoes and remaining 2 tablespoons of olive oil, bring to a boil, season with salt and pepper and return the frog legs to the pan. Reduce to a simmer, cook for another 10 minutes, then remove from heat. Divide evenly among 4 warmed pasta bowls and serve immediately.