Position an oven rack in the lowest position and preheat the oven to 300 degrees F.
Cut the pork shoulder fat-side up into 4 quarters, making sure each quarter has some of the fat cap. Mix together the pepper, sugar and salt in a small bowl, then rub all over the pork.
Put the peaches in the bottom of a large Dutch oven. Rest the pork fat-side up on top of the peaches. Bake until the pork is very tender and shreds easily, 3 1/2 to 4 hours. Transfer to a large bowl and let rest until cool enough to shred, keeping all the juices in the pot. Shred and reserve.
While the pork rests, place the pot with the cooking juices over medium-high heat. Once it starts to bubble, pour in the peach tea and use a wooden spoon to scrape up any browned bits from the bottom and sides of the pot. Return to a boil, reduce the heat to medium and let simmer until the sauce is thickened slightly, 2 to 3 minutes. Add the shredded pork back in the pot and toss to combine.
Serve the pork with slices of Texas toast if desired.