1/4 cup granulated sugar
1 1/8 cups whole milk, warmed
3 teaspoons instant yeast
2 large eggs
1 1/4 sticks unsalted butter, melted
4 cups all-purpose flour, plus more for dusting
1/2 teaspoon salt
4 cups vegetable shortening, for frying (or peanut or safflower oil)
3 cups powdered sugar
1/2 teaspoon salt
1/2 teaspoon vanilla extract