Preheat the Oven

Twenty minutes or longer before baking, set an oven rack in the middle level of the oven and preheat the oven to 375°F/190°C.

Make the Caramel Bun Filling

In a small heatproof bowl, place the raisins and rum. Add the boiling water, cover, and let stand for at least 1 hour so the raisins can become plump with the rum. When ready to fill the dough, place the raisins in a strainer suspended over a small bowl. Lightly press them to remove excess liquid and reserve the liquid for the glaze.

Break and Toast the Pecans

Break the pecans into medium pieces into a strainer. Shake the strainer to remove the nut dust. Spread the pecan pieces evenly on a baking sheet and bake for about 5 minutes to enhance their flavor. Stir once or twice to ensure even toasting and avoid overbrowning. Cool completely. (The whole pecans for the topping [see Note] can be toasted on a separate sheet at the same time.)

In a medium bowl, combine the chopped pecans, brown sugar, granulated sugar, and cinnamon. With your fingertips, break up any sugar lumps.

Roll and Fill the Dough

Have ready a small bowl with the lightly beaten egg.

Turn the dough onto a lightly floured counter. Roll the dough into a 13 to 14 inch wide by 12 inch long rectangle, moving the dough and flouring it as necessary to keep it from sticking. Brush off any excess flour from the top.

Brush the dough, right up to the edges, with the egg. Sprinkle the dough evenly with the sugar mixture and the raisins.

Starting from the top, use your fingers and a long plastic ruler to roll up the dough and to help support the dough as you roll it. (Slip the edge of the ruler slightly under the dough and use it to lift up and roll the dough.) With each roll, dust any flour from the surface of the dough, and press firmly all along the dough roll to keep it from separating. Push together the ends of the roll so that they are the same thickness as the middle and the roll is 12 inches long. Lightly sift flour evenly over the entire roll (not the cut edges).

Cut the Dough and Let It Rise

Dental floss works best to slice the dough, but a sharp serrated knife also works well. To use the dental floss, slide a 9 inch long piece under the dough, cross the two ends over each other, and pull firmly to slice evenly through the dough. Slice the roll into 4 equal pieces and then slice each piece into thirds (each piece will be about 1 inch thick) to make 12 buns.

To make the caramel buns freshly baked for brunch the following day, as soon as they are shaped and placed in the pans, refrigerate them for up to 14 hours. They will take about 2½ hours to rise before baking. To speed rising to about 1½ hours, place them in a proof box with hot water. (See recommended rising environments.)

Set the Ball jars in the centers of the cake pans. There is no need to coat them because the dough does not stick to the glass. Set the buns in the pans, evenly spaced about ¾ inch apart, with the seams facing sideways. Lightly press in any raisins that have popped up. There is no need to press the buns down because they will rise sideways, but very little if at all in height. They start off 1¼ inches from the tops of the pans and will be about the same height after rising. Cover the pans with plastic wrap that has been lightly coated with nonstick cooking spray. Let the buns rise in a warm place (ideally 75° to 85°F/24° to 29°C) for 1 to 1½ hours, or until the sides touch.

Preheat the Oven

Thirty minutes or longer before baking, set an oven rack at the lowest level. Preheat the oven to 375°F/190°C (350°F/175°C if using dark pans).

Bake the Buns

Fill the Ball jars about half full with boiling water. Place the pans on the oven rack and bake for 10 to 12 minutes, or until the buns are beginning to brown. Remove the Ball jars and cover the pans loosely with aluminum foil.

Continue baking for 8 to 10 minutes, or until a skewer inserted into the centers comes out clean. (An instant-read thermometer inserted into the centers should read 180° to 210°F/82° to 99°C.)

While the buns are baking, make the glaze.

Make the Soft Sticky Caramel

See recipe.