In a medium bowl, whisk together butter, egg, and 2/3 cup milk. Add baking mix; whisk just until moistened (do not overmix; a few small lumps are fine).
Preheat oven to 200 degrees. Place a baking sheet in oven to warm. Heat a large nonstick skillet or griddle over medium; very lightly butter surface. Drop batter by 2 tablespoonfuls onto skillet; cook until surface of pancakes have some bubbles and a few have burst, 1 to 2 minutes. With a thin spatula, flip pancakes, and cook until browned on the underside, 1 to 2 minutes more.
Transfer pancakes to baking sheet in oven; cover loosely with aluminum foil. Continue to make pancakes with remaining batter, adding more butter to skillet as necessary (you should have a total of about 12 pancakes).
In a small saucepan, combine chocolate hazelnut spread with remaining 1/3 cup milk. Bring to a simmer over medium-low; whisk until smooth. Serve pancakes topped with chocolate hazelnut sauce and ice cream.
Transfer cooked pancakes to a baking sheet, and keep them in a warm oven until the chocolate hazelnut sauce is ready.