1. In a small bowl, pour bourbon over dried apricots.
2. Scrub sweet potatoes and pierce each in several places with a fork. Place potatoes on oven rack or in a single layer on a baking sheet. Bake in a 350° oven until potatoes are soft when pierced, about 1 1/2 hours. Let stand until cool enough to handle, about 20 minutes.
3. Peel the sweet potatoes and place in a large bowl. Add brown sugar, butter, and vanilla to the bowl and mash with a potato masher or a fork until mixture is only slightly chunky. Stir in apricots and bourbon. Spoon into a shallow 2 1/2-quart baking dish and spread level.
4. Bake, uncovered, until hot in the center, about 30 minutes. Serve warm.
If you like, you can prepare the dish through step 3 up to 2 days ahead; cover airtight and chill. Unwrap and bake as directed in step 4.