Sauté the Garlic: Heat the olive oil in a skillet over medium heat, add the minced garlic, and cook for about 30 seconds.
Cook the Mushrooms: Add the roughly chopped mushrooms and cook, stirring occasionally, for 2–3 minutes.
Deglaze the Mushrooms: Add the Madeira wine, salt, and pepper, then continue cooking and stirring until all the moisture has evaporated and the mushrooms begin to brown, about 5 minutes.
Add the Parsley: Stir the parsley into the cooked mushroom mixture, then transfer everything to a bowl and allow it to cool completely.
Blend the Filling: Place the cooled mushroom mixture and goat cheese in a small food processor and puree until combined, keeping the mixture as smooth or as chunky as desired.
Shape the Croquettes: Transfer the mixture to a bowl and roll it into tablespoon-sized balls, arranging the shaped portions on a plate or baking sheet.
Chill the Croquettes: Place the shaped balls in the freezer for about 15 minutes to firm them before coating.
Prepare the Dredging Station: Place the flour, lightly beaten eggs, and panko breadcrumbs into three separate bowls.
Coat the Croquettes: Remove the chilled balls from the freezer and coat each one first in flour, then in the egg wash, and finally roll it thoroughly in the panko breadcrumbs.
Heat the Frying Oil: Pour vegetable oil into a medium skillet until it reaches about 1/2 inch high, then heat over medium-high heat until the oil shimmers but does not smoke.
Fry the Croquettes: Working in batches, carefully fry the coated croquettes, turning them often, until they are golden brown and crisp, about 3–4 minutes.
Drain the Croquettes: Transfer the fried croquettes to paper towels to drain excess oil.
Season and Serve: Sprinkle the hot croquettes with sea salt and allow them to cool slightly before serving.
