Prepare grill on medium-high heat. Brush corn, cactus and onions with oil. Grill 10-15 min. or until softened and blackened, turning occasionally. Cool slightly. Cut kernels from cobs. Chop cactus and onions into small diced pieces. Combine all vegetables in large bowl.
Mix chimichurri, mayo, lime zest and juice, and cilantro in small bowl; add to vegetables. Mix gently until coated. Reserve some of the cheese; fold remaining cheese into salad.
Garnish with reserved cheese and additional cilantro, if desired. Serve warm or at room temperature.
For extra spice, add 1-2 teaspoons chili powder or as much as 1 jalapeno pepper, finely chopped.
If spring onions are out of season, substitute regular green onions (scallions), which will cook much more quickly on the grill.