Pre-heat oven to 350 degrees and lightly spray or brush a doughnut pan with cooking oil.
Put blueberries, mint leaves and 1 Tbsp sugar in a blender. Blend until puréed. Set aside.
Whisk together flour, baking powder, and salt in a medium bowl. Set aside.
In the bowl of a stand mixer, beat together the butter and remaining sugar until light and fluffy. Add the eggs and mix to combine.
Gently stir the flour mixture into the butter and sugar mixture, alternating with milk. Then stir in the blueberry purée and vanilla extract. Take care not to over-mix.
Evenly distribute batter in a lightly oiled doughnut pan, filling tin almost all the way. I recommend putting batter in a Ziplock bag, cutting off a corner, and piping batter into the doughnut pan.
Bake for 12-14 minutes, until doughnuts are light and springy and just beginning to turn golden at edges.
Remove from oven and let rest in doughnut pan for a few minutes, before removing to a wire rack to cool completely.
When doughnuts are completely cooled, dip them in lime mint icing to coat tops. Allow the icing to cool and harden.