Let eggs stand at room temperature for 30 minutes. Butter and flour a 9 x 5 x 3-inch loaf pan; set aside.
Position a rack in center of oven. Preheat oven to 350 degrees F. In a medium bowl, whisk together the eggs, sugar, butter, milk, and vanilla. In a separate bowl, combine the flour, baking powder, and salt.
In a small saucepan, bring 1 inch of water to simmering over low heat. Place a small bowl over the water, then place chocolate in the bowl. Stir with a rubber spatula until chocolate is melted. Remove from the heat.
Stir the flour mixture into the egg mixture just until combined. Transfer about one-third of the batter (a generous cupful) to a separate bowl. Stir the melted chocolate and instant coffee into the small amount of batter, mixing well. Drop 1/4 cup of plain batter into the prepared pan, then dollop with 2 tablespoons of the chocolate batter. Continue layering both batters. Do not stir the batters in pan together.
Bake cake in center of the oven about 1 hour and 5 minutes, until a wooden pick inserted into center of loaf comes out clean. Cool in pan on a wire rack for 10 minutes. Remove loaf from pan; completely cool on wire rack at least 40 minutes. Before serving, give loaf a quick dusting of powdered sugar to finish.