Build a wood fire or heat a charcoal grill to high heat until it settles into hot coals with some open flame.
Rub the corn lightly with olive oil and season with salt.
Grill the corn over the fire, turning every 2 to 3 minutes, until charred in patches on all sides, about 10 to 12 minutes.
Whisk the tahini, lemon juice, garlic, cumin, and salt together. Add water gradually, whisking, until smooth and pourable. Whisk in the olive oil last.
Let the corn cool for a couple of minutes.
Arrange the corn on a platter and drizzle generously with the tahini dressing.
Scatter with parsley or cilantro, feta if using, and sumac or smoked paprika. Serve with lemon wedges.