Step 1In a small saucepan, heat the Muscat to warm and pour it over the fig halves in a bowl. Let the figs stand 30 minutes to marinate.
Step 2In a large heavy skillet over medium heat, add 2 tablespoons of the olive oil. Add the sliced onions, then stir in sugar, thyme, salt and pepper. Reduce the heat to low, cover and slowly cook until the onions are golden brown, 35 to 45 minutes, stirring occasionally. Keep the onions warm.
Step 3Brush both sides of the bread slices with 1 tablespoon of the olive oil. Grill until lightly toasted, about 1 to 2 minutes, then turn and toast 1 to 2 minutes on the other side. Keep warm.
Step 4Drain the figs and place them on a paper towel. Brush the cut side of the figs with the remaining 1 tablespoon olive oil and put the figs cut-side down on a heated grill pan; cook 2 to 3 minutes until lightly browned. Turn the figs and grill another 2 to 3 minutes until the figs are tender yet retain their shape.
Step 5Divide the warm caramelized onions onto toasted bread slices on a baking sheet. Top with shavings of manchego. Put the sandwiches under the broiler just until the cheese begins to melt, 1 to 2 minutes. Top each sandwich with three fig halves and a sprinkle of fleur de sel on each fig. Serve immediately.