Step 1

Mix cheese, prosciutto (or ham) and tarragon in a small bowl.

Step 2

To stuff chicken breasts, cut a horizontal slit along the thin, long edge, nearly through to the opposite side. Open up each breast and place half the filling in the center. Close the breast over the filling, pressing the edges firmly together to seal. Sprinkle the chicken with 1/8 teaspoon each salt and pepper, then lightly coat with 1 tablespoon cornstarch, shaking off any excess.

Step 3

Heat oil in a large skillet over medium-high heat. Add the chicken and cook, flipping once, until browned, about 6 minutes total. Add broth, reduce heat to maintain a simmer, cover and cook, flipping once halfway through, until an instant-read thermometer inserted in the thickest part of the chicken registers 165°F, about 12 minutes. Transfer the chicken to a plate and cover to keep warm.

Step 4

Add asparagus, peas, spring onions (or scallions) and the remaining 1/8 teaspoon each salt and pepper to the pan. Return to a simmer and cook, stirring occasionally, until the asparagus is bright green and just tender and the liquid reduces slightly, about 4 minutes.

Step 5

Whisk half-and-half and the remaining 1 teaspoon cornstarch in a small bowl. Add to the pan and cook, stirring gently, until the sauce is thickened, about 1 minute. Return the chicken to the pan and turn to coat with the sauce. Slice the chicken and serve with the vegetables and sauce, garnished with more tarragon, if desired.