Combine apricots and 1 cup water in a small saucepan and bring to a boil over medium-high heat. Remove from heat, cover and let stand for 10 minutes. Working over a small bowl, drain apricots well, reserving soaking liquid. (You should have 1/2 cup. Adjust the amount accordingly by discarding some, or adding more warm water).
Transfer apricots to a food processor, add pumpkin and 1 teaspoon of the cinnamon and purée until almost smooth. Cover and refrigerate until chilled.
When soaking liquid is lukewarm (105° to 110°F), sprinkle yeast over the top and let sit until a bubbly foams forms, about 5 minutes. In a large bowl, stir together flour, oat bran, salt and remaining 1 teaspoon cinnamon. Add yeast mixture and almond milk and stir to form a shaggy dough. Turn out onto a floured surface and knead until smooth and elastic, about 5 minutes. Dust the inside of a large bowl with flour and place dough in the bowl. Cover and let sit in a warm spot until dough is doubled in size, 1 1/2 to 2 hours.
Line a baking sheet with parchment paper. On a floured surface, roll out dough into a 14x18-inch rectangle. Spread pumpkin mixture evenly over dough and sprinkle with pecans. Roll up snugly to form an 18-inch log, seam side down. Cut into 24 equal slices, trimming off the end pieces, if you like. Arrange on the prepared baking sheet and let rest in a warm spot. Position the baking rack in the upper third of the oven and preheat to 350°F. Bake until rolls are puffed and golden brown, about 25 minutes. Drizzle with honey (if using) and serve warm.