In a bowl, beat 1/2 cup butter, 2/3 cup sugar, and cardamom with a mixer until fluffy. Add orange peel, egg, egg yolk, and sour cream. Beat to mix well.
Stir together soda, baking powder, 1 cup flour, and diced apricots. Add to butter mixture and stir until evenly blended.
Butter and flour-dust a 5- to 6-cup baking pan or paper baking mold (5 in. wide, 3 in. deep; 7 in. wide, 2 1/2 in. deep; 4 1/2- by 8 1/2 -in. loaf pan; or 8-in. square or round cake pan).
Scrape batter into pan and spread level. If using smaller molds, fill no more than 1/3 full. (You'll have about 1 1/2 cups batter.)
Sprinkle batter evenly (in one or more pans) with 1 tablespoon sugar.
Bake on rack slightly below center in a 350° oven until bread springs back when lightly pressed in center, and just begins to pull from pan sides, 35 to 40 minutes for the whole loaf, less for smaller portions.
Let cool on a rack. Serve warm or cool, inverted from pan, then turned top side up.