Heat oven to 300ºF and position a rack in the center.
Add the cornmeal and salt to a large bowl. Add 2 cups warm water, mixing with your fingers until a soft, moist dough forms. If the dough feels dry, add more water, 1 tablespoon at a time, until dough holds together easily when squeezed.
Add 4 oz (about 1 1/2 cups) of the grated cheddar, and mix until it’s evenly distributed. Cover the bowl with a damp paper towel and let rest for 5 minutes. Combine the remaining grated cheeses in a bowl.
Divide the dough into 8 golf ball-size rounds. Place a sheet of plastic wrap or parchment on top of a work surface. Use your fingers to shape each ball into a flat patty about 5-inches wide and 1/4-inch-thick.
Spread about 1 1/2 tablespoons of the date olive spread into center of one disk, leaving a 1/2-inch gap all around. Add 1/4 of the remaining cheese over the spread, leaving the gap. Place a second disk on top and thoroughly press the edges to seal them well. Press with your fingers to make the arepa as flat as possible and shape the edges of the disk so that the arepa is as even as you can get it. Repeat with the other balls of dough. Chill for 20 minutes.
Set a 12-inch cast iron or non-stick skillet over medium heat and about 1/8-inch oil. When the oil is hot but not smoking, add the arepas, working in batches as needed. Cook, moving them around the pan occasionally, until the first side is golden brown, about 5 minutes. Flip arepas and cook on second side until golden, about 3 to 4 minutes longer.
Transfer to a cooling rack set on a rimmed baking sheet and place in oven while you cook the next batch, if needed.
Serve hot, with any leftover olive-date spread for anyone who wants more.