In a small bowl, pour granulated sugar over strawberry pieces and smash slightly with a fork. This will help draw the juice out of the strawberries to use in the glaze. Cover and set aside.
Preheat your oven to 425°F and grease doughnut pan.
Melt butter in a small microwave-safe bowl. Immerse tea bag in the butter. Allow the tea to seep for about ten minutes. Squeeze as much butter out of the tea bag as possible before discarding the bag.
In a medium bowl, combine 2 tablespoons of the tea-infused butter (this should be almost all of what's left, discard the excess), vegetable oil, granulated sugar, and brown sugar. Whisk until well combined.
Whisk in egg and vanilla extract.
Add baking powder, baking soda, ground nutmeg, and salt. Whisk until smooth.
Add half of the flour, whisking until just combined. Add all of the milk. Mix, and then the rest of the flour. Whisk until just combined.
Place a large plastic bag over a cup and pour batter into the bag. Seal the bag and snip a small piece off of one of the corners. Use the bag to "pipe" batter into your doughnut pan, filling 3/4 of the way full (this should make exactly 6 standard-size donuts).
Bake for 9-11 minutes until donuts are lightly golden and the tops spring back if you press into them. Allow to cool in the pan for 5 minutes before transferring to a rack to cool completely.
Pour sifted powdered sugar into a smallish bowl (you want one that is just large enough to mix the sugar in and fit a doughnut for dipping). Give strawberries another good mash and add 2 tablespoons of the juice to your powdered sugar. If you want seedless, completely smooth icing, run juice through a fine mesh strainer. Whisk until a thick, smooth glaze forms. Dip the doughnuts, rotating them so the glaze covers the entire top half of them.
Add sprinkles to each doughnut immediately after frosting, because this glaze sets quickly and sprinkles may not stick otherwise. Allow glaze to set for 10 to 15 minutes and enjoy!
These doughnuts are best eaten on the first day. If you don't own a doughnut pan, you can make them in a muffin tin. Fill tins 2/3 of the way full (it should make about 10) and cook for 8-10 minutes.