Step 1

Cake:Preheat oven to 350 degrees. Coat a 9-by-5-inch loaf pan with 1 tablespoon butter.

Step 2

In the bowl of a mixer fitted with the paddle attachment, beat remaining 2 sticks butter with sugar on high speed until light and fluffy, about 5 to 8 minutes. Add eggs, one at a time, beating well after each addition. In a small bowl, whisk together condensed milk and vanilla; add to mixer bowl and beat until combined. Remove bowl from mixer. Using a spatula, gently stir in flour, baking powder, and salt. Transfer to prepared pan.

Step 3

Bake until a tester inserted in center comes out clean, about 1 hour. Let cake cool in pan 15 minutes, then invert onto a serving platter and let cool completely.

Step 4

Glaze:Bring condensed milk, vinegar, and lime zest and juice to a simmer in a medium saucepan; cook 1 minute. Remove from heat and pour over cake.