Char the corn on an outdoor grill or over the flame of a stovetop gas burner until browned in spots. Transfer to a cutting board to cool completely.
While the corn cools, make the aioli: Whisk the garlic, mustard, lime juice and egg yolk in a large bowl. Continue whisking constantly while pouring in the oils in a thin, slow stream to form a thick emulsion. Whisk in the salt. The aioli can be covered and refrigerated for up to 2 days.
Slice the kernels off the cobs. Transfer the corn kernels to the bowl with the aioli and add the chives, 1 tablespoon lime juice and a pinch of salt. Mix well, then taste. Add more lime juice and salt to taste.
Spread the corn in a thin, even layer on a serving plate. Sprinkle the cheese, peppers and chile powder on top. Serve immediately.
