How to Make It
Make the pork In a small bowl, whisk the chopped thyme with the brown sugar, salt and spices. Stir in 2 tablespoons of the canola oil until smooth. Rub the spice mixture all over the pork, then refrigerate overnight.
Preheat the oven to 300°. In a large pot, heat the remaining 1/4 cup of canola oil until shimmering. Add half the pork and cook over moderately high heat, turning occasionally, until browned all over, about 10 minutes. Transfer to a large roasting pan. Repeat with the remaining pork.
Add the yellow onions to the pot and cook, stirring occasionally, until softened and just starting to brown, about 8 minutes. Add the wine and cook, scraping the browned bits from the bottom of the pan, until nearly evaporated, about 3 minutes. Add the chicken stock, rosemary sprigs, bay leaves and thyme sprigs. Bring to a boil over high heat, then pour the mixture over the pork. Braise in the oven, turning every 15 minutes, until the pork is very tender, about 3 hours and 15 minutes. Let rest for 15 minutes.
Meanwhile, make the salad Light a grill or preheat a grill pan. In a large bowl, toss the peaches with 1/4 cup of the olive oil and season with salt and pepper. Grill over high heat, turning once, until lightly charred on both sides, about 5 minutes total. Transfer to a work surface and let cool, then cut into small wedges.
In a large bowl, toss the peaches with the cherry tomatoes, cucumber, red onion, vinegar and the remaining 1/4 cup of olive oil. Fold in the mint and basil leaves and season generously with salt and pepper. Serve with the pork.