Trim fat from pork. Sprinkle pork with salt and pepper.
Heat oil in a large deep pot or Dutch oven over medium-high. Brown pork in hot oil on all sides.
Transfer to crockpot.
Hull strawberries and slice in half. Add one cup of them to the crockpot along with the ketchup, vinegar, garlic, rosemary, and hot pepper sauce (if desired).
Cook on low for 6-8 hours or until pork is tender. Remove pork from pot; loosely cover with foil. Let stand 10 minutes.
Skim fat from cooking liquid. Return liquid to large pot; bring to boiling. Reduce heat. Simmer, uncovered, 8 minutes or until reduced to about 1 cup.
Using two forks, shred pork; discard fat. Stir the strawberry BBQ sauce and parsley into pork.