Hydrate the dried fruit and warm the milk: Add milk, raisins, dried apricot pieces, orange zest, vanilla, pumpkin pie spice, and granulated sugar to a small saucepan. Over very low heat, gently warm to 110°F. To make fruit extra soft, you can let this mixture sit for 30 minutes, but it's ready to use once it hits 110°F. Do not overheat.
Activate yeast: Remove the saucepan from heat. Sprinkle yeast onto warm milk mixture and stir to combine. Cover and allow the mixture to sit for at least 5 minutes. When the mixture is foamy with tiny bubbles, it's ready to use.
Prepare the dough: Using a stand mixer with the paddle attachment, add the brown sugar, softened butter pieces, eggs, salt, and 1 cup of flour (the rest will be added in shortly). Add the milk/dried fruit/yeast mixture and be sure to scrape the saucepan so that you get everything. Mix on low speed to combine ingredients.Scrape the sides and then add the remaining 2 1/2 cups flour. Using the paddle attachment, mix on medium-low speed until combined. Occasionally turn the mixer off and scrape down the sides.
Knead dough: Swap the paddle attachment with the dough hook and start kneading the dough on medium speed. If it continues to stick to the sides and the bottom, sprinkle 1 teaspoon of flour at a time while the mixer is running until it no longer sticks. Try to add the least amount of flour needed; the dough should be a little sticky and soft. Knead dough for at least 3 minutes.
1st Rise: Lightly grease a large bowl with the oil. Place the dough in the bowl and turn it so that the entire surface is lightly coated in the oil. Cover the bowl with plastic wrap or a clean kitchen towel and allow the dough to rise in a relatively warm environment for 2 hours or until double in size. If your house is cold, you may set the bowl on a floor heater vent or preheat your oven to 200°F, turn it off, and allow the dough to rise inside with the oven door cracked.
Shape the rolls: Line a baking sheet with parchment paper. Divide the dough into 16 equal pieces. You can do this by shaping it into a square and cutting them into equal-sized squares squares using a pastry cutter or shape knife. Alternatively you can partition into equal-sized pieces and shape each piece into a smooth ball. To do this, pull part of the dough and tuck it underneath. Then, work your way around so that the top looks smooth and the edges are all tucked on the bottom. Arrange the rolls equally spaced on the prepared baking sheet.
2nd Rise: Cover the rolls with plastic wrap or a clean kitchen towel. Allow them to rise for about 1 hour. They should be puffy and larger in size.
Preheat oven to 350°F.
Add the cross: Whisk 1/2 cup of flour and 6 Tablespoons of water together in a small bowl. The mixture should be very smooth and briefly hold it's shape when it drizzles off the whisk. Transfer the paste to a plastic bag and snip a very small corner off for piping. Pipe a line down the center of each row of buns, then repeat in the other direction to create crosses.
Bake the rolls: Bake for approximately 20 minutes or so. The rolls should be golden brown on top. While the buns are cooking, make the glaze (see next step). Remove the buns from the oven.
Add the orange glaze: Whisk the confectioners' sugar, orange juice, and Grand Marnier (if using) together until smooth. Use a pastry brush to cover the buns with the glaze. Serve warm.