Preheat oven to 350 degrees F (175 degrees C). Spread 1 tablespoon olive oil on a baking sheet.
Heat 1 tablespoon olive oil in a skillet over medium heat; cook and stir shallots until translucent
about 3 minutes. Stir garlic
thyme
salt
and pepper into shallots; cook and stir until fragrant
about 2 minutes. Transfer shallot mixture to a bowl; stir in goat cheese
mozzarella cheese
cream cheese
figs
and basil until well combined.
Pound each chicken breast on a work surface until thin. Spoon about 1/4 cup goat cheese mixture onto the middle of each piece of chicken. Roll chicken around the filling and wrap 2 pieces prosciutto around each chicken roll
covering the opening with 1 layer of prosciutto. Place chicken rolls onto the prepared baking sheet
seam-side down.
Bake in the preheated oven for 20 minutes; turn chicken and continue baking until chicken is no longer pink in the center and prosciutto is crisp
about 20 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let chicken stand for 5 minutes before serving.
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