Preheat oven to 375°. Sprinkle pork with salt and pepper.
In a large cast-iron skillet, heat 2 tablespoons oil over medium-high heat. Add pork; cook until browned on all sides, about 3 minutes per side, adding additional oil if needed. Remove from pan. Reduce heat to medium. Add blackberries, ½ cup water, honey, mustard, vinegar, and tarragon. Cook, mashing blackberries with the back of a spoon, until syrupy and reduced, about 10 minutes. Remove from heat, and transfer blackberry mixture to a bowl. Reserve ½ cup blackberry mixture.
Return pork to pan, and spoon a few tablespoons of remaining blackberry mixture over pork. Nestle onions around skillet.
Bake until an instant-read thermometer inserted in thickest portion registers 145°, about 1 hour, occasionally spooning remaining blackberry mixture over pork (about 3 times). Let pork rest for 5 minutes.
Arrange roasted onions and pork on a serving platter. Serve with reserved ½ cup blackberry mixture. Garnish with tarragon and blackberries, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/blackberry-mustard-roasted-pork/