Cut half an apple into chunks. Dice half an onion. Scatter in bottom of slow cooker. Add pork shoulder roast, sprinkle fennel seed over top and season well with salt and pepper. Cook on high for up to 6 hours. When pork is completely cooked and very tender, turn off heat and allow to rest, covered.
When pork is resting, finely dice onion and fennel. Sauté in olive oil on low heat in a large skillet until soft and golden, about 15 minutes.
Peel apple (including remaining half) and chop into small pieces. Add to onion and fennel mixture, along with vinegar and worcestershire. Continue to cook on low until apples are very soft.
Add water as sauce thickens to prevent sticking to pan. Taste and season with salt and pepper.
Prepare slaw by thinly slicing fennel, carrot, cabbage and onion. Dice green onions. Roughly chop frond. Combine oil, vinegar, dijon, celery seed and salt and pepper. Taste and adjust seasoning as needed. Toss dressing with cabbage mixture. Refrigerate until ready to serve. The amount of slaw is enough to top 8 pulled pork buns with extra to serve on the side.
When pork is cooled enough to handle, remove any large areas of fat. Using 2 forks, tear meat into chunks and strips. Add pork to sauce in skillet, toss with sauce and increase heat to medium-high. Without stirring, allow pork to sear until dark and crispy bits are on bottom. Using tongs, turn chunks of meat over to maximize searing.
To serve, lay a leaf of lettuce on the bottom of a bun. Top with a generous amount of pork. Add slaw on top and cover with a second lettuce leaf.
Serve with additional slaw on the side.