Heat the oven to 350°F. Grease and lightly flour two 9×5-inch loaf pans. Set aside.
In medium bowl, sift or whisk together the 3 cups flour, 1 teaspoon baking powder and 1/4 teaspoon salt; set aside.
In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, cream together the 2 1/2 cups sugar and 1 cup unsalted butter until light and fluffy. Add the 1 tablespoon fresh lime juice , 2 teaspoons lime zest and 5 large eggs, beating on high speed for 2-3 minutes.
Add the flour mixture into sugar mixture alternately with 1 cup whole or 2% milk on low speed, beating just until smooth after each addition.
Pour the batter evenly into the prepared pans.
Bake the cakes on the middle rack for 55 to 60 minutes, or until toothpick inserted in center comes out clean. Cool 20 minutes; remove from pan(s) to wire rack. Cool completely, about 2 hours.
When the cakes are cooled, make the glaze.
Whisk together the 2 cups powdered sugar, 2 tablespoons milk and 1 teaspoon lime zest . Add more milk very sparingly until a drizzle-able consistency.
Place the cake on cooling rack with aluminum foil or parchment underneath. Spoon the glaze over cakes and let excess drip below. Let glaze set and then transfer to serving tray.
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