Preheat oven to 350°F.
Using a sharp paring knife, make large X on flat side of each chestnut through shell but not meat.
Soak chestnuts in bowl of warm water for 15 minutes, then drain well.
Arrange chestnuts in one layer in a shallow baking pan, then roast for 15 minutes in middle of oven until shells curl away at X mark.
Wearing protective gloves, peel away shells from chestnuts while still hot.
In large pot boiling water, blanch chestnuts for two minutes, then drain. Using kitchen towel, rub chestnuts to remove skins.
Coarsely chop and reserve.
To make croquetas: Combine cooled chopped chestnuts with all other ingredients in bowl of a stand-up electric mixer. Mix using paddle attachment until well combined. Season with salt and pepper to taste. Do not whip the mixture, as you do not want to aerate it.
Cover croqueta mixture and put into refrigerator to chill for at least 2 hours.
Once croqueta mix is chilled, form into one-inch balls.
Beat eggs in a small bowl and set aside. Spread flour in a shallow bowl, then spread breadcrumbs in another shallow bowl.
Working in batches of 4 to 5 croquetas at a time, roll balls in flour to coat, gently shaking off excess flour.
Dip balls in egg, turning to coat and letting excess drip off, then roll in breadcrumbs and set aside on a plate.
Chill uncovered for 30 minutes.
Heat 1 1/2 inches of oil in a 3-quart pot until it registers 350°F on thermometer.
Working in 4 batches, fry croquetas, turning if necessary, until browned, about 1 to 2 minutes per batch.
Transfer with a slotted spoon to paper towels to drain, then transfer to a baking pan and keep warm in oven while frying remaining croquetas. Serve.