Warm the milk to 110° F (43° C) in a small bowl and stir in the 1 teaspoon of sugar plus the yeast. Set aside for around 5 minutes or until the yeast is foamy and active.
In a mixer bowl, add the remaining sugar, the flour, and salt, mixing briefly with a dough hook. Once the yeast mix is ready, add it and the lightly beaten egg to the mixer bowl and turn on to low for about 3 minutes until the dough is mostly mixed.
Add all the butter and continue to mix for another 3-4 minutes or until the dough has smoothed and appears elastic. If the dough is still too sticky, add up to 1 more tablespoon of flour.
Place the dough in a greased bowl, cover with plastic, and let rise for about an hour, until doubled in size.
For the topping:
Generously grease a 9x2 round pan with butter. Sprinkle the pecans and currants (or raisins) evenly around the bottom of the pan.
Add the remaining topping ingredients to a saucepan and warm over medium heat. Stir every once in a bit until the everything reaches a roiling foamy boil. Remove from heat and pour the caramel over the pecans and dried fruit. Set aside to cool.
For the filling:
Mix the brown sugar and cinnamon in a small bowl, breaking up the lumps.
For the rolls:
Tip the risen dough onto a lightly floured counter, giving it a knead or two to deflate the air. Either using a floured rolling pin or by hand, manipulate the dough into a 10” square, aiming for squared corners.
With a spoon, evenly spread the apple butter over the dough then sprinkle it with the brown sugar/cinnamon filling.
Carefully roll up the dough and pinch the seam. Using a serrated knife, cut the dough in half then cut each half into quarters for a total of 8 rolls. With the exposed spiral side up, place each piece in the pan atop the pecan currant caramel.
Cover the pan loosely and allow to rise again for about a half hour. Halfway through, preheat the oven to 375° F (190° C).
Remove the covering and bake the rolls until golden brown for about 28-30 minutes then let cool on a rack for about 5 minutes. With a knife, loosen the rolls in the pan around the edges, place the serving plate on top and flip everything over onto the plate. Carefully remove the pan.
Serve warm or store covered and serve at room temperature or reheat in the microwave.