Allow brioche dough to come to room temperature and line work surface with a sheet of parchment paper. Lightly flour parchment paper and transfer dough to parchment. Lightly flour dough and roll into a 9×12rectangle that is ¼ inch thick. Arrange the rectangle in the landscape format, so the 12 side is in front of you. With a small offset spatula, spread apricot jam evenly over dough. Starting from the short side, begin tucking and rolling the edge of the dough over the sugar, keeping it snug. It’s important to roll the dough tightly, so the foundation is strong and it won’t unravel later when the dough is cut. Continue to roll the dough similar to a jelly roll. Lift the parchment paper to help roll the dough up. Press on the seam to make sure it sticks. Wrap parchment around the rolled dough and freeze until firm, at least 1 hour. Preheat oven to 375°. Use a pastry brush to coat a 6-cup muffin tin with softened butter. Sprinkle 2 teaspoons sugar in each cup. Hold the tin upright at a slight angle and turn it clockwise to shake the sugar so that each compartment is coated with sugar. Remove morning bun log from freezer and slice into 6 equal portions, about 2 inches thick. Place each bun in sugar-lined muffin cup, cut side up. Leave dough to proof in warm place until it is soft and pillowy, rising above rim of molds, about 1 hour. Bake until golden brown, about 36 minutes, rotating halfway through. Cool for 10 minutes before un molding. Use a small offset spatula to loosen buns. If caramel is too cool to un mold properly, return tin to oven for 5 minutes and un mold. Toss in remaining ¼ cup sugar to coat. Serve warm.