Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper. Lightly grease the parchment to help the fritters brown and release cleanly.
Prep the apples. In a bowl, toss the diced apples with lemon juice, brown sugar, and cornstarch. Set aside. The cornstarch helps soak up extra juice so your fritters don’t spread too much.
Whisk the dry ingredients. In a large bowl, combine flour, granulated sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
Mix the wet ingredients. In a separate bowl, whisk the eggs, buttermilk, yogurt, melted butter, and vanilla until smooth. If the butter starts to firm up, no stress. Keep whisking; it will come together once combined with the dry ingredients.
Make the batter. Pour the wet mixture into the dry. Stir gently with a spatula until most of the flour disappears. It should look thick and a little sticky. Fold in the apples and any juices left in the bowl.
Portion the fritters. Using a large spoon or a 1/4-cup scoop, drop mounds of batter onto the prepared sheet, spacing them about 2 inches apart. For that classic craggy fritter shape, don’t smooth the tops too much. A few rough edges help the exterior crisp.
Bake. Place the sheet on the middle rack and bake 12 minutes. Rotate the pan, then bake another 6–9 minutes, until the fritters are golden at the edges and set in the centers. A toothpick should come out with a few moist crumbs, not wet batter.
Cool slightly. Let the fritters rest on the pan for 5 minutes, then transfer to a wire rack. The steam will escape and keep the bottoms from getting soggy.
Make the glaze. In a small bowl, whisk powdered sugar, 2 tablespoons milk, vanilla, salt, and melted butter if using. Add a splash more milk if needed. You’re aiming for a thick but pourable glaze that ribbons off the whisk.
Glaze and serve. Spoon or drizzle the glaze over the warm fritters and let it set for a couple of minutes. Eat while still warm. If you like a thicker shell, glaze twice.