Directions

1. Melt butter in a medium skillet over medium-low heat; add shallots. Cover and cook, stirring occasionally, until softened, about 10 minutes. Add thyme and continue cooking until onions are caramelized, about 5 minutes. Remove from heat and set aside.
2. Spread 1 1/2 teaspoons mustard on one side of a slice of bread. Top with a slice of cheese, 2 ounces ham, 1/4 of the shallot mixture, and another slice of cheese. Spread 1 1/2 teaspoons mustard on a second slice of bread and place mustard side down on top of cheese to form a sandwich. Repeat process three times with remaining mustard, bread, cheese, ham, and shallots.
3. Brush top and bottom of each sandwich with olive oil. Place in a panini grill and press until bread is crisp and brown, and cheese has melted slightly, 9 to 10 minutes. If using a grill pan, preheat over medium-high heat. Place a heavy pan on top of sandwiches and press down. Cook, turning once, 2 to 3 minutes per side. Cut sandwiches in half and serve immediately.