Leek-and-Mushroom Croquettes

2 leeks, white and tender green parts only thinly sliced

1/4 pound(s) shiitake mushrooms, stemmed and caps thinly sliced

Salt and freshly ground pepper

1 teaspoon(s) chopped thyme

1 teaspoon(s) chopped oregano

3 tablespoon(s) all-purpose flour, plus more for coating

1 cup(s) milk

1/2 cup(s) shredded Gruyere

1/4 cup(s) freshly grated Parmigiano-Reggiano

2 large eggs beaten with

2 tablespoons of water

1 1/2 cup(s) panko, Japanese bread crumbs

Vegetable oil, for frying