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