Preheat the oven to 400°F (200°C). Line a metal baking sheet with foil and lightly grease it if desired.
Arrange the frozen beef patties in one layer on the baking sheet, leaving space between them. Do not thaw them first.
Whisk the mayonnaise, ketchup, and yellow mustard in a small bowl until smooth. Spoon the sauce over the tops of the frozen patties, spreading it to the edges.
Bake on the middle rack for 20 minutes. Carefully turn each patty, spoon pan sauce and drippings over the tops, and bake 10 to 15 minutes more.
Check the center of each patty with a meat thermometer; ground beef should reach 160°F (71°C). If needed, continue baking in 3- to 5-minute increments. Rest 3 to 5 minutes before serving with the pan sauce.