In a mixing bowl, combine 2 cups all-purpose flour, 1/2 cup granulated sugar, 1 tablespoon baking powder, and 1/2 teaspoon salt to prepare the dough.

In another bowl, whisk together 2/3 cup milk, 2 large eggs, 1/4 cup melted unsalted butter, and 1/2 teaspoon vanilla extract until smooth.

Pour the wet ingredients into the dry ingredients and mix until just combined, taking care not to overmix.

Heat oil in a deep frying pan or deep fryer to 375°F (190°C) using a cooking thermometer.

Roll out the dough and cut out 12 donuts using a donut cutter or two cookie cutters, ensuring each has a center hole.

Carefully place the donuts into the hot oil and fry for 2 to 3 minutes on each side until golden brown.

Remove the donuts from the oil and place them on a cooling rack to cool completely.

In a bowl, mix 1 cup powdered sugar, 2 tablespoons milk, and 1 teaspoon green food coloring to make the glaze, then dip each cooled donut into the glaze and decorate with chocolate chips and white icing.