The Kirby Super Star mode in which Kirby eats the most food is Gourmet Race. It is a competitive racing game where Kirby races King Dedede through three courses while collecting food along the way.
Gourmet Race scores players for both eating food and finishing quickly. The winner is determined by the combined results across the courses, so speed is not the only objective. Players can race against King Dedede, compete against a recorded ghost of a previous run, or run a course alone to chase the fastest time.
The title is sometimes described as a minigame because it is a self-contained activity within Kirby Super Star, but the game itself lists Gourmet Race among its separate game modes. Dyna Blade and Milky Way Wishes are longer adventure modes with their own progression and objectives, while Boss Rush is not one of the original Kirby Super Star modes. Gourmet Race's emphasis on food and racing makes it the canonical answer.