Prep time: 15 minutes
Total time: 30 minutes
1 cup|250 ml heavy cream
1/2 cup|125 ml strong brewed coffee, cooled to room temperature
1/2 teaspoon sea salt
1 large egg, lightly beaten
4 tablespoons unsalted butter
4 slices country-style ham
2 slices day-old brioche or thick-cut white bread
4 slices gruyere cheese
2 quail eggs
1. Heat oven to 400°F. In a medium bowl, whisk together the cream, 1/4 cup coffee, the salt, and 1 large egg. Set aside.
2. Melt 1/2 tablespoon butter in a large nonstick skillet over medium-high. Working in batches, cook the ham, flipping once, until slightly crisped, 1 to 2 minutes. Deglaze each batch with 1 tablespoon coffee.Transfer the ham to a plate and set aside.
3. Wipe the skillet clean and reduce the heat to medium. Dredge the bread slices in the coffee and cream mixture. Add another tablespoon of butter to the skillet to melt. Fry the bread, flipping once, until lightly golden, about 2 minutes. Lay the ham and cheese on one slice of bread and top with the other slice of bread to create a sandwich. Transfer to a cutting board.
4. Cut the sandwich in half. Using a 1-inch round cutter, cut circles in the middle of each. Transfer the mini sandwiches and their circles to a baking sheet. Crack a quail egg into each circle and bake until the eggs are just set, 2 minutes more. Serve immediately.