Make the chaffle batter by cracking the eggs into a food processor or powerful blender. Add the cream cheese cut into 1-ounce pieces along with a pinch of salt. Use the pulse button to carefully blend the ingredients until the eggs and cream cheese are broken up. Then, you can turn your appliance on to blend the chaffle batter into a lump-free, frothy liquid. You may need to scrape the batter down with a spatula and blend more than once to complete the batter.
Choose a cast-iron or non-stick skillet to heat on your stove to medium-low heat. Melt ½ teaspoon coconut oil per chaffle you’re cooking in the skillet. Once the oil is heated, pour ¼ cup of batter per chaffle into the skillet. Let the batter slowly spread into a circle. After the chaffle cooks a little, use a spatula to gently fix any thin or misshapen edges. Sprinkle ½ teaspoon shredded pepper jack cheese and a pinch of minced chives over the center of the batter.
Reduce the heat as necessary once you see how quickly your batter is cooking. You may need to use only a low heat setting if you’re cooking just one chaffle at a time. Once the chaffle has turned golden brown on one side and the batter has settled, flip the chaffle over to finish cooking on the other side. Transfer the finished chaffle to a plate to cool, and repeat the cooking steps to finish making all your chaffles. When you’re done, leave the chaffles aside to cool and return your skillet to your stovetop.
Wipe your skillet clean, if necessary, to remove any excess coconut oil. To make one grilled cheese, melt ¼ tablespoon of butter in the skillet over medium-low heat. Place one chaffle down flat in the butter, and sprinkle ½ ounce shredded cheddar over the top. Let the chaffle cook until it’s golden brown on one side, then use a spatula to fold the chaffle in half to create a folded grilled cheese sandwich. Flip the grilled cheese back and forth until it’s grilled on both sides and the cheese is melted. Repeat this step until all the grilled cheese sandwiches are made.