Step 1: Cut a deep pocket in the side of each chicken breast. Wrap a slice of prosciutto around some cheese slivers to obtain a roll about 1/4-inch thick. Repeat to obtain 8 rolls.
Step 2: Stuff 2 of these prosciutto and cheese rolls into each chicken breast. (The rolls should run lengthwise.) Pin the pocket shut with an oiled toothpick. Lightly brush the outsides of the chicken breasts with olive oil and season generously on both sides with salt and pepper.
Step 3: Make the Saffron Butter: Soak the saffron threads in 2 teaspoons warm water for 5 minutes. In a small saucepan on the stovetop or the side burner of your grill, melt the butter over medium heat. Add the shallot or garlic and cook until just beginning to brown, 2 minutes. Do not let burn. Stir in the saffron mixture.
Step 4: Set up the grill for direct grilling and preheat to high. (We used grapevine trimmings for building the fire. Have lots on hand; they burn fast.)
Step 5: When ready to cook, brush or scrape the grill grate clean and oil it well. Arrange the chicken breasts on the grill running on a diagonal to the bars of the grate. Grill until browned on both sides and cooked through (the internal temperature should be 165 degrees), about 4 minutes per side, giving each breast a quarter turn after 2 minutes to lay on a crosshatch of grill marks. Start basting the chicken breasts with Saffron Butter after 2 minutes and continue basting.
Step 6: Transfer the chicken breasts to a platter. Drizzle the remaining Saffron Butter over them and sprinkle with chopped chives. Serve with grilled asparagus, if desired.
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Steven Raichlen’s Project Fire is a production of Maryland Public Television, Barbacoa, Inc., and Resolution Pictures. © 2018 Barbacoa, Inc.