For the pork: In a small bowl whisk together 2 Tbsp of olive oil, vinegar, garlic, Italian seasoning, honey, fennel, red pepper, and salt. Set aside.
Heat the remaining 2 Tbsp of oil on high in a rondeau or similar pan. Sear pork on all sides. Pour olive oil mixture and water over top of seared pork and bring to a boil, stirring. Reduce to a simmer and cover until pork is very tender, 2-2 1/2 hours.
Remove pork from pan and allow to cool slightly. Strain remaining liquid into a small sauce pot. Simmer uncovered until it has reduced by a third. Shred pork and add back to liquid. Keep warm.
For the aioli: Whisk together all ingredients until evenly distributed. Refrigerate until needed.
For the build: Toast ciabatta rolls. Spread each side with aioli. Place 4 oz of pork on the base of each roll and top with 2 Tbsp of hot peppers and 1/4 cup of arugula. Place 4 slices each of the asiago on the top of the roll and melt either under a salamander or broiler and place on top of the sandwich. Serve warm.
