Toast the walnuts in a small sauté pan over medium heat, tossing often, until golden brown and fragrant, 3 minutes. Let cool, then coarsely chop.
Cook fregola in a large pot of boiling salted water according to package directions. Drain, but do not rinse; spread out on a baking sheet to cool.
Set your grill on to medium-high heat. Rub corn with a tablespoon of oil and season with salt and pepper. Grill, turning occasionally, until lightly charred and tender, 10 minutes or so depending on size of corn ears. Transfer to a platter and let cool.
Brush cheese with tablespoon oil and grill, turning once, until lightly charred on each side, about 5 minutes. Transfer to platter with corn and let cool.
Cut the kernels from corn cobs and place into a large bowl. Add green onions, parsley, basil, mint, walnuts, and fregola. Tear Halloumi into bite-size pieces. Add to bowl and toss to combine.
Whisk together the dressing ingredients (lemon juice, vinegar, and oil). Pour over salad and toss to mix thoroughly. Season with salt, pepper, and more lemon, if desired.