Trim and discard rind from Brie round. Cut Brie into slices, about 1/4-inch.
Spread 1 side of each piece of bread with a thin layer of red pepper jelly.
Cover half the pieces with Brie slices, evenly distributing all the Brie among the 4 slices.
Top Brie with strawberries, basil, and turkey. Place remaining bread slices on top, red pepper jelly side down. Brush outside of bread slices with melted butter.
Cook, in batches in a heated Panini press until golden brown, about 2-3 minutes. If you don't have a Panini press, use a grill pan or large skillet and use a spatula to press down on the top of the sandwiches. Flip to cook both sides evenly.
Notes
Note: If you don't have a panini press, you can use a grill pan or nonstick skillet and flip the sandwich over to brown both sides.