Rub roast with salt and pepper and let sit at room temperature at least 1 hour.
Place a rack in lower third of oven; preheat to 225°. Line a rimmed baking sheet with 2 layers of foil (don’t skimp on the foil unless you really enjoy scrubbing pans after dinner). Arrange rosemary sprigs in center of baking sheet and set a wire rack over top.
Pulse rosemary leaves in a food processor until finely chopped. Add anchovies and oil and process until a thick paste forms. Wearing gloves if you have them, rub paste over entire surface of roast, pressing into meat to adhere. If you have a leave-in probe thermometer, insert so tip of probe is in center of roast (the thermometer sensor is in the tip). Set roast, fat side up, on wire rack and roast meat until probe thermometer or an instant-read thermometer registers 118° for medium-rare, 3–4 hours. Let cool 45 minutes; internal temperature will rise to 130°.
Increase oven temperature to 475°. Return meat to oven and roast until fat is browned, 10–15 minutes.
Do Ahead: Roast can be seasoned 3 days ahead. Wrap with plastic and chill.
Conserva and Assembly
Cook blackberries, sugar, and salt in a large wide saucepan over medium-high heat, stirring occasionally, until thick and syrupy, 40–50 minutes. Stir in vinegar and pepper. Remove from heat and let sit until ready to serve.
Serve roast with warm conserva and butter alongside.
Do Ahead: Conserva can be made 3 days ahead. Let cool; cover and chill.