Place potato in large saucepan; fill with cold water to cover. Bring to a boil. Cook about 6 min. until potato begins to soften. Stir in broccoli and garlic; cook another 3 to 5 min. until potato, broccoli and garlic are tender. Drain well; place on tea towel or paper towels to soak up excess moisture. Cool completely.
Preheat oven to 200˚C (400˚F). Line 2 baking sheets with parchment paper brushed with oil. In food processor, pulse potato, broccoli and garlic until smooth. Pulse in breadcrumbs, Parmesan and green onions to combine. Switch to a spatula and stir in Cheddar.
Roll out “dough” into ½-in. (1-cm) thick ropes; cut into 1-in. (2.5-cm) pieces. Make 48 pieces. Arrange on lined baking sheets, spacing 2 in. (5 cm) apart. Bake 15 to 20 min., turning once, until golden brown. Serve with ranch dressing for dipping, if desired.