2 small ribs celery, finely chopped
1 small carrot, grated
1 medium shallot, finely chopped
1/4 teaspoon powdered chicken bouillon
1/4 teaspoon celery seeds
2 tablespoons all-purpose flour
1/4 teaspoon garlic powder
1 cup plus 2 tablespoons milk, divided
1/3 cup frozen peas
freshly ground black pepper
1/4 cup panko breadcrumbs
1 pound ground chicken
nonstick cooking spray
4 hamburger buns, lightly toasted
In a cast-iron skillet, melt 2 tablespoons of the butter over medium heat. Add the celery, carrot, shallot, bouillon, celery seeds and 1/4 teaspoon salt and cook, stirring occasionally, until softened, about 7 minutes. Transfer to a large bowl and let cool to room temperature.
Meanwhile, in a small saucepan, melt the remaining 2 tablespoons butter over medium heat. Add the flour and garlic powder and cook, whisking, for about 1 minute. Gradually add 1 cup of the milk and bring the mixture to a simmer, whisking continuously. Continue to simmer, whisking, until thickened, about 2 minutes. Add the peas, 1/2 teaspoon salt and a generous amount of pepper. Remove from the heat and cover to keep warm.
Mix the panko into the cooked vegetables, then stir in the remaining 2 tablespoons milk and let stand for 5 minutes. Add the ground chicken, 1 teaspoon salt and a dash of pepper.
Form the chicken mixture into four 3/4-inch-thick patties. Spray the skillet and one side of the patties with nonstick spray.
Heat the skillet over medium-high heat, then place the patties in the skillet, sprayed-side down, and spray the tops of the patties. Reduce the heat to medium, then cover and cook for 2 minutes. Flip the patties and cook, uncovered, until they are cooked all the way through and the centers are firm, about 2 minutes more.
Serve on the buns, topped with the pea gravy with extra gravy on the side.