Prepare the gougeres: Preheat the oven to 425 degrees F and line 2 baking sheets with parchment paper or silicone mats. In a large saucepan, combine the butter, salt and 1 cup water. Stir over high heat until the butter melts completely, then remove the pan from the heat and add all the flour at once. Stir vigorously with a wooden spoon until smooth, then transfer to a mixer fitted with a paddle attachment. Beat on medium speed and add the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Beat in the grated cheese.
Transfer the dough to a pastry bag, or use 2 wet spoons to drop neat 1-tablespoon mounds onto the prepared baking sheets, spacing them about 1 inch apart. Bake for 25 to 30 minutes, until golden and crisp. When done, turn off the oven and let the gougeres dry out in the oven with the door ajar to keep them nice and crisp.
Cook the apples for the filling: Peel the apples and discard the core; cut into 1/2-inch dice. Melt the butter in a large saute pan over high heat. When foaming, add the spices. They will toast instantly and become fragrant; add the apples and saute for 3 to 4 minutes, until browned. Add 2 tablespoons water, the honey and lemon juice. Cook for 3 to 4 minutes, or until the liquid is reduced and the apples are tender. Set aside to cool slightly.
Set a clean saute pan over medium heat. Add enough olive oil to coat the pan; when hot, fry the sage leaves until crisp and almost transparent, about 1 minute. Drain on paper towels. Add the prosciutto pieces to the same pan in a single layer (work in batches, if necessary). Cook for 1 minute on each side to crisp them up. Drain on paper towels.
To assemble, carefully tear off the top third of each gougere and spoon in some warm apple filling. Top with a sage leaf and a piece of prosciutto and season lightly with fleur de sel. Drizzle with olive oil and sprinkle with black pepper.
Photographs by Yunhee Kim
Recipe courtesy Tyler Florence for Food Network Magazine