Arrange three bowls for dredging, placing flour in one, breadcrumbs in another, and the egg in the third, then beat the egg. The egg should look uniform enough to coat the cheese evenly.
Stir the garlic powder through the breadcrumbs. The seasoning should disappear into the crumbs without visible clumps.
Cover each burrata ball with flour, then egg, then breadcrumbs, supporting it in one palm while applying crumbs with the other hand. Use light pressure so the delicate pouch keeps its rounded shape.
Inspect the coating and repeat the egg-and-breadcrumb layers wherever coverage looks thin or crumbs will not adhere. The finished surface should feel evenly crumbed, with no slick, damp patches showing through.
Fill a suitable saucepan with 3 to 4 inches of oil, deep enough to cover the burrata, and heat it to 325°F using a thermometer. Leave ample space above the oil for bubbling when the cheese enters.
Ease the burrata into the oil with a slotted spoon and fry for 2 to 3 minutes, lifting it after the first minute to inspect the crust. If it already looks too dark, hold it out of the oil while the temperature drops before returning it.
Lift out the burrata when the exterior is golden, checking the result by about 3 minutes. The shell should look crisp, with the cheese warmed inside rather than spilling into the saucepan.
Transfer the fried cheese to the paper towel-lined plate to drain. The surface should lose its excess oil while the breadcrumb shell stays intact.