Cream-Filled Doughnuts

For the Doughnuts:

• 1 cup whole milk, warm
• 1/4 cup granulated sugar
• 2 teaspoons active dry yeast
• 2 1/2 cups all-purpose flour
• 1/2 teaspoon salt
• 2 large eggs, beaten
• 6 tablespoons unsalted butter, softened
• Vegetable oil, for frying

For the Cream Filling:

• 1 cup heavy cream
• 1/2 cup powdered sugar
• 1 teaspoon vanilla extract

For Coating:

• 1/2 cup granulated sugar

Instructions: