Stir together first 6 ingredients. Rub brown sugar mixture over roast; place roast in a lightly greased 6-qt. slow cooker.
Whisk together mustard and next 3 ingredients. Pour mustard mixture over top of roast. Cover and cook on LOW 8 to 10 hours (or on HIGH 4 to 6 hours) or until meat shreds easily with a fork. Let stand 15 minutes. Shred pork with a fork; stir until sauce is incorporated.
Bake slider buns according to package directions. Split buns. Spoon 1/4 cup barbecued pork and 1/4 cup Lowcountry Slaw onto each bun bottom. Cover with tops of buns, and serve immediately.
To make ahead, prepare recipe as directed, and let pork cool completely (about 1 hour), stirring occasionally. Freeze in an airtight container up to 3 months.
We tested with Pepperidge Farm Classic Sliders Mini Buns.