Slice the tomatoes into even ½-inch rounds. Lay on a paper towel for 1 minute to remove excess surface moisture.
Season both sides of each slice with salt, pepper, and a pinch of sugar.
Dredge each slice in the flour, coating both sides evenly, and shake off the excess.
Heat the olive oil in a heavy skillet over medium-high heat for 2 minutes, until shimmering and hot.
Add the tomato slices in a single layer without crowding the pan; work in batches if needed.
Fry for 2 minutes per side, until the flour turns deep golden brown, flipping only once.
Add the sliced garlic to the oil during the last minute of cooking so it softens without burning.
Transfer the fried tomatoes to a paper towel–lined plate to drain for 1 minute.
Move to a serving plate, scatter with the softened garlic and torn fresh basil, and serve warm.