Step 1

Stir together herbes de Provence, salt, and pepper in a small bowl; rub mixture evenly over roast. Chill, uncovered, at least 12 hours or up to 24 hours. Let roast stand at room temperature 1 hour.

Step 2

Heat oil in a large skillet over medium-high. Cook roast on all sides until well browned, 3 to 4 minutes per side. Transfer roast to a 6-quart slow cooker, rib side down. Add beef broth and wine; cover and cook on LOW until a meat thermometer inserted in thickest portion registers 130°F to 135°F for medium-rare, 3 to 3 1/2 hours. (For medium, cook until a meat thermometer inserted in thickest portion registers 140°F to 145°F, about 4 hours.)

Step 3

Transfer roast to cutting board, and loosely cover with aluminum foil; let stand 30 minutes before carving. Meanwhile, pour red wine mixture from slow cooker through a fine mesh strainer into a bowl, discarding solids. Transfer strained mixture to a small saucepan. Bring to a boil over medium-high, and cook until slightly reduced, about 2 minutes. Remove from heat; stir in butter until melted. Serve roast with butter-wine sauce and sea salt for sprinkling.