In bowl, combine carrot, garlic, onion, oats, 2 tbsp (25 mL) of the milk, the Worcestershire sauce, and half each of the salt and pepper. Add beef; mix well. Shape into two patties, each 1 inch (2.5 cm) thick.
Place patties on greased grill over medium heat; close lid and grill, turning once, until digital thermometer inserted sideways into centre reads 160°F (70°C), 12 to 14 minutes.
Meanwhile, in small saucepan of boiling salted water, cover and cook potatoes until fork-tender, about 15 minutes. Drain; mash potatoes until smooth. Stir in remaining milk, salt and pepper.
Place one patty on serving plate; spread ¾ cup (175 mL) mashed potatoes over top. Top with remaining patty; spread remaining mashed potatoes over top and sides of “cake.” Press panko into sides of cake.