Step 1

Combine pork, oil, vinegar, garlic, rosemary, honey, fennel, red pepper flakes, 1 Tbsp. salt, and 1 cup water in the insert of slow cooker. Turn pork several times with tongs to coat and mix ingredients. Slide insert into base, cover, and cook over high heat until pork is very tender and shreds easily, about 4 hours. If programming your slow cooker, set for 4 hours on high, then set to warm after that (while pork is cooking, make the broccoli rabe).

Step 2

Transfer pork to a medium bowl and let rest until cool enough to handle. Pour cooking liquid through a fine-mesh sieve into a medium saucepan; discard solids. Let liquid settle so fat rises to the top, then pour off and discard all but a thin layer of fat. Bring liquid to a simmer over medium heat and cook, stirring occasionally, until reduced by about a third, 12–18 minutes.

Step 3

Meanwhile, shred pork with your fingers or 2 forks, discarding any large bits of fat. Season with salt.

Step 4

Set aside 1 cup cooking juices for serving, then add shredded pork to saucepan with remaining juices and toss to coat and rewarm pork.

Step 5

Do Ahead: Pork can be cooked 2 days ahead. Shred and add to reduced juices, then let cool, cover, and chill. Reheat over low.

Step 6

Bring a large pot of salted water to a boil over high heat. Fill a large bowl with ice water and have at the ready. Add broccoli rabe to pot and cook just until stems are tender, about 2 minutes. Using tongs, transfer broccoli rabe to bowl of ice water and agitate to rapidly cool down. Drain and pat dry on paper towels. Transfer to a cutting board and slice into 1" pieces on the diagonal, all the way from stem to leaves.

Step 7

Heat oil in a large skillet over medium. Cook garlic and red pepper flakes, stirring often, until garlic is golden around the edges, about 2 minutes. Increase heat to medium-high and add broccoli rabe; season with salt. Cook, tossing constantly, until leafy bits are just starting to crisp slightly, 7–10 minutes.

Step 8

Divide pork among bottoms of rolls. Top with provolone, shingling slices. Spoon broccoli rabe over, then squeeze lemon wedges over broccoli rabe. Close up sandwiches and cut in half. Serve with reserved juices for dipping.

Step 9

Do Ahead: Broccoli rabe can be blanched 1 day ahead. Pat dry, cover, and chill.