Whisk all dressing ingredients together. Taste and adjust until tangy, smoky, and bright. Set aside.
Soak diced red onion in cold water for 5 minutes. Drain and pat dry.
Heat a skillet over the highest heat until smoking. Add corn in a single layer with no oil. Do not stir for 2 minutes. Toss and cook 2 more minutes until charred and golden. Cool for 5 minutes.
Add tomatoes, red onion, jalapeño, cilantro, and parsley to the cooled corn. Pour dressing over and toss well.
Fold avocado through gently with two or three movements. Keep pieces intact.
Scatter cheese on top if using. Finish with a final squeeze of fresh lime.
Serve immediately with extra cilantro and lime wedges.