Bring a large pot of water to a boil. Add the corn and a generous pinch of salt and return to a boil. Remove from the heat, cover and let stand for 5 minutes. Drain the corn and let cool slightly.
Meanwhile, in a small bowl, whisk the mayonnaise with the lime and lemon zests and juices along with the 1 tablespoon of olive oil, the mustard, garlic and cayenne. Season the citrus aioli with salt.
Light a grill or preheat a grill pan.
Brush the corn with olive oil and season with salt.
Grill over high heat, turning occasionally, until lightly charred all over, about 5 minutes.
Transfer to a plate and let cool slightly, then cut the kernels off the cobs; discard the cobs.
In a large bowl, toss the corn with the softened butter. Stir in the citrus aioli.
Add the queso fresco, cotija, parsley and cilantro.
Season with salt and pepper and serve warm.