How to Make It
Preheat grill to high (450°F to 500°F). Toss together oil and 20 ounces of the radishes in a medium bowl. Place radishes on grates coated with cooking spray; grill, covered, turning occasionally, until grill marks appear and radishes are tender in the middle, 10 to 12 minutes. Place radishes on a cutting board, and cut in half lengthwise. Cover to keep warm.
Thinly slice remaining 4 ounces radishes using a mandoline slicer or a sharp knife. Whisk together butter, lemon juice, thyme, salt, and pepper in a small bowl. Toss together grilled and raw radishes in a medium bowl; drizzle with dressing, and sprinkle with feta.