Add the dried apricots and currants (or whatever dried fruit you are using) to a medium microwave-safe bowl with the apple juice or water. Cover with plastic wrap and microwave for 30-45 seconds. The plastic wrap will expand then shrink wrap the bowl, sealing in the hot liquid and helping to soften the dried fruit. Set aside to soak.
Meanwhile, warm the milk in the microwave for 45 seconds until warm but not scalding hot. Add 1 teaspoon of the sugar and the yeast, then let it proof for 5-10 minutes until the yeast is nice and foamy. If using instant yeast, you can skim this step of warming the milk and proofing the yeast and instead move on to the next step immediately.
In the bowl of a stand mixer fitted with the paddle attachment, combine the proofed yeast and milk mixture, eggs and egg yolk (save the egg white for later to use as an egg wash), remaining sugar, orange zest, vanilla, cinnamon, allspice, nutmeg, cardamom, salt, and 2 cups of the flour. Mix until combined, then switch to the dough hook and add the remaining flour.
Knead the dough on medium speed until the flour is combined, then start adding the softened butter, one tablespoon at a time. Let the dough knead for about a minute between adding each tablespoon of butter, until all of the butter has been kneaded into the dough and it is nice and smooth. It will be around 7-8 minutes of kneading and the dough will be very sticky, soft, and elastic. Some of it will still be sticking to the bottom of the bowl, although if it is looking really sticky and unmanageable, go ahead and add an extra 1/2 cup of flour to it. The less flour you can manage with the better though for the softest buns.
Add the dried fruit and any soaking liquid that has not been absorbed and knead this into the dough until the fruit is evenly dispersed. You might need to scrape the bowl and turn the dough over by hand once or twice to get the fruit mixed in all the way as my dough hook can't always get the job quite done without a little help.
Transfer the dough to a large, greased bowl and cover with plastic wrap. Set in a warm place to rise until almost doubled in size, around 1-2 hours. This dough may take a bit longer to rise than other yeast doughs and it might not completely double in size because the added fruit and fats inhibit the rise a bit and slow the process down. But it should still be nice and puffy looking. I usually stick my dough in a sunny spot by the window or on the back of the counter by the stove where it is warm.
Turn out the dough onto a clean surface and use a bench scraper, sharp knife, or pizza cutter to divide the dough into 12 evenly sized pieces. Shape into balls by pinching the ends underneath to create a nice, smooth surface on top and place them into a grease 9x13-inch baking dish. Cover with plastic wrap and set in a warm place to rise for 30-60 minutes until they are nice and puffy and touching each other.
While the buns are rising, preheat the oven to 375°F. When the buns are puffy and ready to go in the oven, whisk the reserved egg white together with 2 teaspoons of water and gently brush over the top of each bun. Bake for 25 to 30 minutes until the buns are a nice golden brown on top and cooked through (but don't overbake or the buns will be dry).