Preheat the oven to 400 degrees . Brush a small, rimmed baking sheet with 1 tbsp. oil. Butterfly the chicken by slicing horizontally into the long, thick side of the breast, being careful not to slice all the way through. Open the chicken like a book and place, cut side up, on a piece of plastic wrap. Using a mallet, pound to 1/4 inch thick. Layer with the Brie, apricots and thyme, leaving a 3/4-inch border; season with salt and pepper. Starting with one long edge, tightly roll the chicken into a log; tie with 4 pieces of kitchen string.
On a plate, combine the panko and pecans. Brush the chicken all over with the egg white and roll in the panko-pecan mixture to coat, pressing to adhere. Transfer the chicken, seam side down, to the prepared baking sheet. Bake until an instant-read thermometer inserted in the center registers 160 degrees , 30 to 35 minutes.
Meanwhile, in a medium skillet, heat the remaining 1 tbsp. oil over medium-high. Add the radishes; season and cook, stirring occasionally, until crisp-tender and browned in spots, about 8 minutes. Add the radish leaves and garlic; cook until the leaves wilt, about 1 minute.
Remove the string from the chicken and cut crosswise into 8 slices. Divide the chicken and radishes between plates.