Preheat oven to 400 degrees. Spray a roasting pan with cooking spray.

Heat 1 tablespoon olive oil in a large skillet over medium heat. Add half of garlic and cook until fragrant, about 2 minutes. Add spinach and cook until wilted, stirring occasionally. Remove from heat and stir in 1 tablespoon tarragon. Transfer to a bowl to cool. (You can put in the freezer for a minute to expedite.)

Toss asparagus with 1 tablespoon olive oil and salt and pepper. Set aside.

Season chicken breasts with salt and pepper. Cut a slit into the side of each piece, being careful not to cut all the way through.

When spinach mixture has cooled down, add ¾ cup shredded cheese and stir to combine. Stuff each chicken breast with ¼ of the spinach-cheese mixture.

Heat remaining 2 tablespoons olive oil in the same skillet used for the spinach over medium-high heat. Add stuffed chicken and cook until browned on each side, 3-4 minutes per side. Turn off heat and transfer chicken to roasting pan.

Bake for 10 minutes. Remove pan from oven and add the asparagus to the pan. Sprinkle remaining cheese over the top of chicken. Bake 10-15 minutes longer, depending on size of the pieces, until chicken reaches internal temperature of 165 degrees.

While chicken is baking, make the pan sauce. In the same skillet used to brown the chicken, melt butter over medium heat. Add shallot and cook until soft, 3-4 minutes, stirring often. Add remaining garlic and cook until fragrant, about 2 minutes. Add wine and scrape up any brown bits from the bottom of the pan. Cook for 2 minutes. Add broth, cream, and remaining 1 tablespoon tarragon. Stir to combine. Cook, stirring occasionally, until sauce thickens, about 5 minutes. Taste and add salt and pepper as necessary.

To serve: Divide chicken and asparagus between serving plates and spoon the pan sauce over chicken.