Mince the mushrooms finely in a food processor or with a very sharp knife. (I used the chopping blade on my Magic Bullet.)

Melt butter in a large frying pan and add mushrooms, salt, and pepper. Cook until no liquid remains, and the mushrooms are very fragrant, about seven minutes. Cool completely.

Spoon a tablespoon of mushrooms onto the edge of each cheese slice, then roll up and lay seam side down on a tray. Place into the freezer until ready to bread.

Set up a breading station with the flour, eggs, and bread crumbs, and season each one with salt and pepper. Double-bread each cheese stick: flour, egg, bread crumbs, flour, egg, bread crumbs.

Return to freezer for a minimum of one hour, or up to three months.

Fill a pot halfway with oil and heat. Fry in batches for three minutes or until golden brown.

Drain on paper towels and serve immediately, along with marinara sauce for dipping.