In a large skillet, melt 1 tbsp. butter over medium. Add the panko, season with salt and pepper and cook, stirring occasionally, until browned, about 3 minutes; transfer to a small bowl.
In the same skillet, melt the remaining 2 tbsp. butter over medium. Add the carrots, leeks and garlic; season. Cook over medium, stirring occasionally, until the vegetables start to soften, about 3 minutes. Add the flour and stir until the vegetables are coated, 2 minutes. Add the cream and stock and bring to a boil. Cook over medium heat, stirring occasionally, until the liquid is reduced by half, about 8 minutes.
Add the chicken, peas and 3/4 tsp. tarragon. Cook the ragu over medium-low heat, stirring occasionally, until the chicken is cooked through, about 8 minutes; season.
Meanwhile, in a large pot of boiling, salted water, cook the noodles to al dente; drain. Return to the pot and toss with the ragu; season. Divide the pasta among bowls and top with the toasted panko and the remaining 3/4 tsp. tarragon.