How to Make It
Preheat the oven to 400°. Drizzle the olive oil on a large, rimmed baking sheet. Arrange the squash and sweet potatoes on the baking sheet, cut sides down. Roast for about 45 minutes, until tender and lightly browned on the bottom. Let cool.
Scoop the squash and potato flesh into a large bowl and mash well. Stir in 2 of the egg yolks, the whole egg, the cheese and the thyme and season with 1 teaspoon of salt and 1/4 teaspoon of pepper. Refrigerate until chilled, about 1 hour.
In a shallow bowl, beat the remaining 4 egg yolks with the water. Spread the flour and bread crumbs in two shallow bowls; season the bread crumbs with salt and pepper. Line a baking sheet with wax paper or plastic wrap. Working in batches of 4, scoop rounded tablespoons of the croquette mixture into the flour. Roll into balls, dip in the egg wash, coat with the bread crumbs and place on the baking sheet. Repeat to form the remaining croquettes. Let the croquettes stand at room temperature for at least 10 minutes and as much as half an hour to firm up slightly before frying.
In a large deep skillet, heat 1 inch of the vegetable oil to 350°. Line another baking sheet with paper towels and a rack. Add the croquettes to the hot oil in batches, taking care not to crowd the pan, and fry over high heat, turning once, until golden brown. Using a slotted spoon, transfer the croquettes to the rack to drain. Serve hot with the Bitter Orange Compote.