In a food processor, combine the flour, sugar, salt, and cold butter; pulse a few seconds until crumbly. Add the ice water one tablespoon at a time, pulsing just until the dough comes together with small pieces of butter still visible.
Turn the dough out and shape into a disk with your hands. Wrap in plastic and refrigerate until chilled and firm.
Meanwhile, make the filling: toss the apple slices with the brown sugar, cinnamon, and lemon juice.
Roll the chilled dough into a large circle on a floured surface. Arrange the apple slices in the center, leaving a 1½–2 inch border. Fold the edges up and over the filling. Brush the crust and apples with the melted butter, then drizzle the apples with honey.
Place the galette on parchment in the air fryer basket. Cook at 330°F (165°C) for 12 minutes, or until the crust is golden brown and the apples are tender.
Let rest a few minutes, then slice, serve, and enjoy — delicious warm with vanilla ice cream.