To make the sauce: Melt the butter in a medium heavy-bottomed saucepan over medium heat. Add the onion and cook, stirring occasionally, until golden brown, about 5 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Stir in the tomato puree, peach preserves, balsamic vinegar, bourbon, honey, mustard, and hot red pepper sauce and bring to a simmer. Reduce the heat to low and simmer, stirring often, until thickened and reduced by about one quarter, 25 to 35 minutes. Remove from the heat and let cool.
Position racks in the center and top third of the oven and preheat the oven to 425°F.
To prepare the chicken: Mix the paprika, salt, thyme, black pepper, and cayenne pepper in a small bowl. Toss the chicken and oil in a large bowl to coat. Sprinkle with the spice mixture and toss again. Divide the wingettes between 2 large rimmed baking sheets.
Bake for 20 minutes. Remove from the oven and flip the wingettes over. Switch the positions of the baking sheets from top to bottom and continue baking until the wings are golden brown, about 20 minutes more. Transfer the wingettes to a large heatproof bowl. Add the sauce and stir gently to coat the wingettes. Pour off the fat from the sheets. Return the wingettes to a single sheet.
Bake until the sauce is glazed, 5 to 10 minutes. Transfer the wingettes and sauce to a platter and serve.