Heat the oven to 325°F (165°C) with a rack in the middle. Grease a 3-cup mini loaf pan, about 6 x 3 inches, with the 1 tbsp softened butter, reaching into every corner. Dust with the 1 tbsp flour and tap out the excess.

Beat the 6 tbsp butter with the brown sugar and granulated sugar on medium-high speed until pale and fluffy, 2 to 3 minutes, scraping the bowl once.

Beat in the egg and then the egg yolk, mixing well after each, until the batter looks glossy. Mix in the 1/2 tsp vanilla. A slightly separated look is fine.

Whisk the 3/4 cup flour, 1/8 tsp salt and baking powder together in a small bowl.

Mix on low speed, adding the flour mixture in three parts and the 1/4 cup evaporated milk in two, beginning and ending with flour. Stop as soon as the last streak of flour disappears. The batter will be thick.

Scrape the batter into the pan, smooth the top and tap the pan twice on the counter. Bake for 45 to 55 minutes, until the top is deep golden and a toothpick pushed into the center comes out clean or with a few dry crumbs. Tent loosely with foil if the top browns too fast.

Cool the cake in the pan for 10 minutes, run a thin knife around the edge and turn it out onto a wire rack. Let it cool for about 15 minutes, until just warm.

Melt the 2 tbsp glaze butter in a small saucepan over medium heat. Add the 1/4 cup brown sugar, 1 tbsp evaporated milk and the pinch of salt, bring to a boil, and let it bubble for 1 minute, stirring, until smooth and glossy. Take the pan off the heat.

Stir in the 1/4 tsp vanilla and 1/2 cup powdered sugar until smooth. Add more powdered sugar a tablespoon at a time until the glaze falls from the spoon in a thick ribbon.

Pour the glaze slowly over the just-warm cake so it runs down the sides. Let it set for 20 to 30 minutes before slicing into 4 thick slices.