Start by cooking the mushrooms and drawing out their liquid: melt the butter in a large sauté pan over low heat
Add the shallot and sauté for 2-3 minutes until softened, then add the garlic and sauté for an additional 30 seconds
Add the mushrooms, then season with salt and freshly cracked black pepper (the salt will help draw out the moisture from the mushrooms)
Cook for 8-10 minutes, stirring occasionally, until the mushrooms are cooked through and most of the liquid released has evaporated
Increase the heat to medium to ensure any remaining liquid evaporates and the pan is almost fully dry
Add the white wine, scrape to deglaze the pan, then simmer over medium heat for 2-3 minutes or until the wine has reduced and the liquid has fully evaporated again (see Note 2)
Stir in the fresh parsley and season with additional salt to taste, then remove from the heat and set aside to cool
While the mushrooms are cooling, make the béchamel: in a medium saucepan, melt the butter over low heat
Add the flour and whisk, then cook for 4-5 minutes or until the roux is lightly golden and toasted
Slowly pour in the milk while whisking continuously
Increase the heat to medium-low and bring to a very gentle boil, whisking continuously, until thickened
Once thickened, reduce the heat back to low and stir in the salt, black pepper and nutmeg
Add half of the Parmesan cheese and whisk until fully melted and smooth, then add the remaining Parmesan and whisk again until smooth
Combine the béchamel and the mushrooms in either pan or a heatproof bowl and stir (see Note 5)
Chill the mixture in the fridge for at least 1-2 hours or until completely cooled (this makes shaping the croquettes much easier)
When the mixture has cooled and hardened, shape into 6 large equal sized balls or ovals (see Note 3)
Shape the mushroom mixture around the mozzarella cheese sticks, ensuring the cheese is fully covered
Transfer to a plate and freeze for 2 hours until firm (this makes them easier to handle and makes breading much easier)
Once the croquettes are cold and easy to handle, add the flour, egg and breadcrumbs to 3 separate shallow bowls; beat the egg
One at a time, dip the croquettes in the flour, then in the beaten egg, then in the breadcrumbs, pressing to ensure all sides are well coated; transfer breaded croquettes to a plate
Freeze for 10-15 minutes while the oil heats up
Heat the oil over medium-low heat in a large sauté pan until shimmering; it should be around 325℉/170℃ and no hotter than 350℉/180℃ (see Note 6)
Fry the croquettes in 2 or 3 batches for around 45 seconds on each side or until golden brown and crispy
Using a spider strainer or metal tongs, transfer fried croquettes to a paper towel lined rack – try to avoid using a plate if you have a rack so they don’t sit in the oil and stay perfectly crispy