Preheat oven to 350°F (175°C) for 10 minutes. Lightly butter a 9x13-inch baking dish and set aside on a clean counter. Checkpoint: Oven is fully preheated when you see heat shimmer through the oven window.

Peel and slice 6 medium Granny Smith apples into 1/4-inch thick slices (should take about 8–10 minutes). Place sliced apples in a large mixing bowl.

Add 1/4 cup granulated sugar, 2 tablespoons brown sugar, 1 tablespoon all-purpose flour, 1/2 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, 1/8 teaspoon sea salt, 2 tablespoons fresh lemon juice, and 1 teaspoon vanilla extract to the apples.

Using a large spoon or your hands, toss the apples gently for 2–3 minutes until every slice is evenly coated with the sugar and spice mixture. The apples should look glistening and uniformly pale brown. Checkpoint: All apples are coated when you don't see white patches on any slices.

Pour the apple mixture into the prepared baking dish, spreading it evenly with the back of a spoon. The filling should reach about halfway up the sides of the dish.

In a separate medium bowl, combine 1 cup old-fashioned rolled oats, 1/2 cup all-purpose flour, 1/3 cup packed brown sugar, 1 cup sharp cheddar cheese (shredded), 1/4 teaspoon sea salt, and 1/4 teaspoon cayenne pepper. Stir with a fork for 1 minute until the cheese is distributed throughout. Checkpoint: The mixture should look like sandy, flecked crumbs with no clumps of cheese.

Cut 1/2 cup cold unsalted butter into small cubes (about 1/2-inch each). Add all butter cubes to the oat mixture at once.

Using your fingertips, rub the butter into the oat mixture for 4–5 minutes, working quickly so the butter stays cold. The texture should resemble coarse breadcrumbs with some pea-sized pieces of butter visible. If the mixture becomes warm or starts to stick, refrigerate it for 5 minutes and continue. Checkpoint: The topping is ready when it's crumbly with no large clumps and bits of butter are still visible.

Sprinkle the oat topping evenly over the apples in the baking dish. Use your hands to gently pat it down so it holds together loosely and doesn't fall into cracks. The topping should not be completely packed or it will be dense instead of crispy.

Place the baking dish on the center oven rack and bake for 40–50 minutes at 350°F (175°C). The topping should turn golden brown and the apple filling should bubble and release steam at the edges. If the topping browns too quickly (before 35 minutes), tent it loosely with foil and continue baking. Checkpoint: The crisp is done when the topping is a deep golden brown and you see fruit juice bubbling at the edges of the dish.

Remove from the oven using oven mitts and place on a heat-safe trivet or thick towel on your counter. DO NOT TOUCH—it is extremely hot.

Let the cheesy apple crisp cool undisturbed for 10–15 minutes at room temperature. This allows the apples to set slightly and the cheese to firm up, making it easier to scoop. As it cools, the topping will continue to crisp and harden. Checkpoint: Wait until you can hold your hand 2 inches above the dish for 3 seconds without pulling it away.

Scoop the crisp into bowls with a large spoon, ensuring each serving has apples, filling, and topping together. Serve warm with vanilla ice cream, whipped cream, or plain yogurt if desired.