Pull off small pieces of goat cheese and roll into dime-sized balls.
Pour panko bread crumbs into a bowl; roll goat cheese balls in crumbs until coated.
Heat olive oil and garlic in a saucepan over medium-high heat. Cook and stir goat cheese balls in the hot oil for 15 to 30 seconds. Scoop them back into the bowl of bread crumbs to create a second coating. Arrange on a rimmed baking sheet.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Broil goat cheese balls, shaking baking sheet every 30 seconds to 1 minute to ensure even browning, about 2 minutes.
Toss arugula with remaining 3 tablespoons olive oil, balsamic vinegar, salt, and pepper in a large bowl. Divide among 4 serving bowls; top each bowl with warm goat cheese balls.