Heat the oven to 350°F (175°C) with a rack in the middle and grease an 8 x 4 inch loaf pan with the 1 tsp butter. Zest 2 limes with a fine grater, then juice them to get 3 tablespoons.

Whisk the flour, baking powder and salt together in a bowl.

Beat the 4 tbsp butter and the granulated sugar with a mixer on medium-high speed until pale and fluffy, 2 to 3 minutes. Beat in the egg, 1/2 tsp of the vanilla and 1 tsp of the lime zest until smooth.

Mix in the flour mixture in two parts, alternating with the 1/2 cup milk, on low speed until just smooth with no dry streaks. The batter will be thick.

Scrape the batter into the pan, smooth the top and bake for 30 to 35 minutes, until the top is pale gold, springs back when pressed and a toothpick comes out clean or with a few moist crumbs.

Cool the cake in the pan for 10 to 15 minutes, until warm but not hot. Meanwhile, whisk the condensed milk, lime juice, 1/4 cup milk and 1/2 tsp of the lime zest until smooth. It thickens slightly within a minute.

Poke holes about 1 inch apart across the warm cake with the handle of a wooden spoon, pushing most of the way down without touching the bottom of the pan.

Pour the filling slowly over the cake in three rounds, waiting 2 to 3 minutes between rounds, until it has sunk into the holes and the surface looks wet and glossy. Cover and refrigerate for at least 4 hours or overnight, until cold and set.

Whip the cream with the powdered sugar and the remaining 1/2 tsp vanilla in a cold bowl until soft peaks form, 1 1/2 to 2 minutes. Spread it over the chilled cake.

Sprinkle with the remaining 1 tsp lime zest and the graham cracker crumbs, then cut into 4 slices.