Bring a large sauce pot of lightly salted water to a boil.

• Let the braised pork shoulder come to room temperature.
• Shuck the corn; break or cut the ears in half.

Add the corn to the boiling water and cook until tender, 2 to 3 minutes, then drain. Return the corn to the pot and add the butter, swirling to coat. Season with salt and pepper and cover to keep warm.
While the water heats and the corn cooks, prepare the pork.

In another large sauce pot over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the pork and cook, stirring once or twice, until the meat begins to crisp around the edges, 2 to 3 minutes. Add 1½ cups of the vinegar sauce base (set aside the remaining vinegar sauce base for the slaw). Season with as many chile flakes as you like and cook, stirring once or twice, until the sauce is bubbling, 1 to 2 minutes. Remove from the heat, cover, and keep warm.
While the pork heats, prepare the coleslaw.

In a medium bowl, stir together the cabbage, carrots, 1 teaspoon oil, and as much of the remaining vinegar sauce base as you like. Season to taste with salt and pepper.

• Cut the buns in half.

Place the bun bottoms, cut sides up, on a work surface. Top with the pork and cabbage slaw. Close with the bun tops.

Transfer the sliders to individual plates. Serve the corn and any remaining slaw on the side.

Kids can!

• Shuck the corn.
• Stir together the coleslaw.
• Assemble their own sliders.
• Serve the meal.
• Sweep the floor.