01 -
Mix fontina cheese, prosciutto (or ham), and tarragon in a small bowl.
02 -
Cut a horizontal slit along the thin, long edge of each chicken breast, nearly through to the opposite side. Open each breast and place half the filling in the center. Close the edges firmly to seal. Sprinkle with 1/8 teaspoon each salt and pepper, then coat lightly with 1 tablespoon cornstarch, shaking off excess.
03 -
Heat 2 tablespoons of oil in a large skillet over medium-high heat. Add the chicken and cook, flipping once, until browned, about 6 minutes.
04 -
Add chicken broth to the skillet. Reduce heat to maintain a simmer, cover, and cook, flipping once halfway through, until an instant-read thermometer inserted in the thickest part registers 165°F, about 12 minutes. Transfer the chicken to a plate and cover to keep warm.
05 -
Add asparagus, peas, spring onions (or scallions), and the remaining 1/8 teaspoon each salt and pepper to the skillet. Simmer and cook, stirring occasionally, until the asparagus is bright green and tender and the liquid slightly reduces, about 4 minutes.
06 -
Whisk half-and-half with the remaining teaspoon of cornstarch in a small bowl. Add to the pan and cook, stirring gently, until the sauce thickens, about 1 minute.
07 -
Return the chicken to the pan and turn to coat it with the sauce. Slice the chicken and serve with the vegetables and sauce. Garnish with tarragon, if desired.