Heat oven to 450°F. Rub beef with olive oil, salt, garlic powder, and pepper. Set on a rack in a small roasting pan.
Roast 15 minutes; lower oven to 325°F. Cook 25 to 40 minutes more until center reaches 145°F. Rest 15 minutes, including at least 3 minutes before cutting.
Cut roast crosswise into 2 shorter pieces; place in a shallow container. Refrigerate promptly about 3 hours until 40°F or colder; prep time includes chilling.
Slice cold beef very thinly across the grain. Mix softened butter and Dijon; spread on one face of every bread slice.
Divide cheddar over 4 bread slices. Add loosely folded beef and dry cornichon slices; close with remaining bread. Halve sandwiches.
Serve cold or refrigerate at 40°F or below; use ice packs for transport.