Bring a large pot of water to a boil and add the baking soda—you'll see it foam up like crazy. Add your potato pieces and let them cook until they're super tender, about 15-18 minutes. Test with a fork; they should practically fall apart. Drain really well in a colander and let them sit for a minute to get rid of excess moisture.
While the potatoes cook, mince your garlic and warm the half-and-half in a small saucepan over low heat. Don't let it boil—just make it warm enough that it doesn't shock the potatoes later. This step makes everything blend smoother, trust me on this.
Transfer your drained potatoes to a large mixing bowl and add the butter while they're still hot. Mash them until you've got mostly smooth but still some small lumps—I personally like texture, not wallpaper paste. This takes about 2-3 minutes of mashing with a good masher.
Fold in the warm half-and-half, minced garlic, paprika, salt, and pepper. Mix gently until everything's incorporated and the mixture is creamy but still holds its shape. Stir in the cheddar cheese and keep mixing until melted. Don't panic if it looks a little loose right now—it'll firm up as it sits.
Beat the egg in a small bowl, then fold it into your potato mixture. This might seem weird, but the egg creates that fluffy, cloud-like texture when it hits the air fryer heat. Mix until the egg disappears completely into the potatoes.
Scoop the mixture onto a parchment-lined air fryer basket in 6 mounds, spacing them about an inch apart. Drizzle with olive oil and sprinkle with a little extra salt and pepper on top. These need room to crisp up, so don't crowd the basket.
Air fry at 400°F for 20-22 minutes until the tops are golden brown and the edges look crispy. You want that contrast between the crunchy outside and creamy inside. Top with fresh parsley right before serving while everything's still warm.