Preheat oven to 350°F. Spray wells of mini-bundt pan with non-stick spray. (See Tip 2)
Working in a large bowl, rub the sugar and lemon zest together with your fingertips until the sugar is moist and fragrant. Add butter. Beat on high until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Scrape the sides and bottom of the bowl and beat briefly to re-combine any residue.
Add salt and baking powder; beat until combined.
Add the flour to the batter in three parts alternately with the milk, starting and ending with the flour. Mix until everything is well combined.
Using a 1 ¾-inch ice cream, drop batter into wells of prepared pan. (See Tip 3)
Bake in preheated 350°F oven for 17 to 18 minutes or until top springs back when lightly pressed.
Remove the pan from the oven and let the bundtinis cool in the pan for 5 minutes. After 5 minutes, remove from pan to a wire rack.
While the bundtinis are still hot, dip each one on lemon syrup. Let cool completely.
When the bundtinis are completely cooled, transfer to brioche paper cups. Spoon the frosting into a piping bag fitted with a #4B open star tip. Swirl the frosting from the outside to the center top of each of the bundtinis.