Copycat Lard Lad's Big Pink Doughnut

• ½ cup milk
• ¼ cup water
• ¼ cup vegetable oil
• 1 egg , room temperature
• 1 teaspoon salt
• ¼ cup sugar
• 3 cups bread flour , divided
• 1 package Active Dry Yeast

For Frying

• 6 cups canola or vegetable oil

For the pink glaze

• 1 cup powdered sugar
• 1-2 teaspoon milk , add 1 at a time
• 5 drops pink gel food coloring
• 1 TBS Rainbow sprinkles