Preheat oven to 500°F.
Place roasted chestnuts, butter, garlic, thyme, sage, lemon zest, 2 teaspoons salt, and 1 teaspoon pepper in a food processor.
Blend until paste forms.
Place rib roast fat side up on cutting board.
Loosen fat cap with a sharp knife, leaving one side attached.
Spread chestnut paste evenly under the fat cap with hands.
Press fat back into place.
Season outside of roast generously with kosher salt and black pepper.
Place roast bone-side down on a rack in a roasting pan.
Roast at 500°F for 15 minutes.
Reduce oven temperature to 325°F.
Continue roasting about 15 minutes per pound, until thermometer reads 120°F in thickest part.
Tent loosely with foil if crust darkens too quickly.
Remove roast from oven.
Rest 30 minutes before carving.
Cut twine, remove rib bones, and slice meat across the grain into desired thickness.
Serve with pan juices and seasonal sides.