Whisk milk, eggs, and 1 tablespoon vegetable oil together in a bowl until thoroughly combined. Sprinkle in the chestnut flour 1/4 cup at a time, mixing well to avoid lumps, until batter is a liquid consistency. Whisk vigorously; pour through a fine strainer to remove any lumps.

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Heat cooking oil in an 8-inch crepe pan over medium-high heat. Pour in 1/4 cup of batter; swirl batter around to cover the entire surface. Cook until the edges have browned and are easily loosened with a spatula, 2 to 3 minutes per side. Transfer to a serving plate. Repeat with remaining batter.