Make the croquette base
In a small bowl, whisk together the flour, salt, pepper, and nutmeg. Heat the oil and butter in a medium
saucepan over medium heat until the butter is melted. Add the flour all at once and cook, stirring constantly, until lightly golden, about 3 minutes. Slowly whisk in the milk and cook until the mixture is smooth and slightly thickened, 2–3 minutes.
Finish the base
Use a spoon or
silicone spatula to stir in the prosciutto (or peas) and cheese. Cook until the mixture pulls away from the sides of the pan, about 2 minutes. Smooth evenly into a pie plate or 9×9-inch baking dish and cool for 15 minutes. Cover with plastic wrap and refrigerate for at least 2 hours, or up to 24 hours, until firm.
Form and bread the croquettes
Beat the eggs in a shallow dish and season with salt and pepper. Place the breadcrumbs in another bowl and season generously with salt and pepper. Roll 1 tablespoon of the filling at a time into balls (you should have about 28 croquettes, roughly 1½ inches wide). Dip each ball into the egg, letting the excess drip off, then roll in the breadcrumbs, shaking off excess. Arrange on a baking sheet and refrigerate for at least 1 hour and up to 8 hours.
Make the spicy maple drizzle
Combine the maple syrup, chili flakes, and a pinch of salt in a small microwave-safe bowl and heat until just warm, about 15 seconds, to infuse the chili. Let cool to room temperature.
Fry the croquettes
Heat 3 cups of oil (about 2 inches deep) in a
braiser or Dutch oven over medium-high heat until it reaches 350°F or a breadcrumb dropped into the oil sizzles and turns golden immediately. Working in batches of 4, fry the croquettes, turning occasionally, until golden brown and crispy, 2–3 minutes. Drain on paper towels and cool slightly. If frying ahead, rewarm on a foil-lined baking sheet at 400°F for 10 minutes.
Build the Croquettembouche
On the base of a
serving dome or a plate at least 9 inches in diameter, arrange a circle of 8 croquettes. Fill the center with 4 croquettes. For the next layer, make a circle of 6 croquettes and fill it with 2 croquettes. Add a layer of 4 croquettes, then 3, and finish with a single croquette on top. Drizzle generously with the spicy maple syrup and serve immediately.