Heat the oven to 425°F and set a large ovenproof 12-inch skillet on the middle shelf.

Heat the garlic with 1 Tbs. of the oil in a large skillet over medium-high heat until it sizzles steadily, about 1½ minutes. Add the arugula and cook, tossing, until it wilts, about 2 minutes. Remove from the heat and, using a spatula, press the greens and pour off any accumulated liquid.

Transfer the arugula to a food processor along with the pecorino, breadcrumbs, pine nuts, and currants. Pulse to finely chop.

Cut the chicken in half almost all of the way through and set each piece flat (so that each breast now looks like an open book). Using a meat pounder or the heel of your hand, pound the chicken to flatten. Rub both sides of the chicken with 1 Tbs. of the oil and sprinkle with half of the thyme and with 3/4 tsp. salt and ½ tsp. pepper.

Spoon and press the arugula mixture onto the top of each chicken piece. Roll the chicken over onto itself so it forms a tight roll. Secure with a toothpick and repeat with the remaining pieces of chicken.

Using an oven mitt, remove the skillet from the oven, and add 1 Tbs. oil. Return the pan to the oven and roast the chicken until it cooks through–an instant-read thermometer inserted into center of the thickest piece should register 165°F–about 12 to 15 minutes.

Carefully remove the toothpicks and then serve, drizzled with the balsamic glaze.