Preheat a charcoal or gas grill for direct grilling over medium heat (350°).

Grill bratwursts for 10 to 12 minutes or until bratwursts reach 165°, turning often. If bratwursts begin to flare up, reduce heat to low. Cut each bratwurst in half lengthwise; cut each again in half crosswise. Set bratwurst pieces aside.

For sauce, melt butter in a small saucepan over medium heat. Whisk in flour. Gradually whisk in milk; continue whisking until smooth. Cook and whisk for 1 to 2 minutes or until sauce is thickened. Remove from heat.

Whisk 1 tbsp. mustard, salt, white pepper and nutmeg into sauce; whisk in cheese until melted. Set sauce aside.

Brush a medium rimmed baking pan with olive oil. Place bread slices, in a single layer, in prepared baking pan. Spread each bread slice with a 1 Tbsp. of cheese sauce, spreading sauce to the edges.

For each sandwich, place 4 bratwurst pieces, cut sides down, lengthwise on top of half of the sauce-covered bread slices. Spread bratwursts with remaining 4 tsp. mustard; top with pickle slices. Place remaining bread slices, sauce sides down, on top to enclose sandwiches.

Place baking pan with sandwiches over direct heat. Close grill lid. Grill for 2 to 4 minutes or until bottoms are toasted. Turn sandwiches over; spread each with 1 Tbsp. of cheese sauce and grill, covered, for 2 to 4 minutes more or until bottoms are toasted and cheese sauce is melted.

To serve, cut each sandwich in half diagonally.