Heat 2 tablespoons olive oil in a large skillet over medium heat. Sauté 1 medium finely chopped onion until translucent, about 3-4 minutes. Add 2 cloves minced garlic and stir for 1 minute until fragrant.
Season with salt, pepper, and 1/4 teaspoon nutmeg, then add 1 pound Wagyu ground beef. Cook until browned, breaking it apart with a spoon.
Stir in 3 tablespoons all-purpose flour and cook for 1 minute to remove raw taste. Whisk in 1 cup whole milk until the mixture thickens into a creamy, thick mass.
Transfer to a bowl and refrigerate for 2 hours to firm.
Scoop chilled mixture and form into 1-inch logs or balls.
Set up a breading station: dust croquettes lightly with flour, dip in 2 beaten eggs, then coat with 1 cup Panko breadcrumbs.
Refrigerate breaded croquettes for 30 minutes to set.
Heat 1-inch vegetable oil in a cast iron skillet to 350°F (175°C). Fry croquettes in batches, 1-2 minutes per side, until golden brown.
Drain on paper towels using a slotted spoon.
In a small bowl, combine 1 cup mayonnaise, 1 teaspoon smoked paprika, 1 tablespoon lemon juice, and 1 clove minced garlic.
Add a pinch of salt and whisk until emulsified.