Preheat your oven to 350°F for about 5 minutes. Lightly butter a 9-inch round baking dish or 8x8-inch square baking dish to prevent sticking. Checkpoint: Oven is ready when the dial reaches 350°F.

Bring a large pot of water to a boil. Carefully lower fresh peaches into boiling water for 45 to 60 seconds until the skin begins to split slightly. Remove with a slotted spoon and place in a bowl of ice water for 1 to 2 minutes to cool. Checkpoint: Peach skin should slip off easily when you run your thumb across it.

Once cooled, peel the skin off the peaches by gently rubbing with your thumb. Slice each peach in half, remove the pit, then cut into 1/4-inch thick slices. You should have about 4 cups of sliced peaches. Checkpoint: All peaches should be evenly sliced to roughly the same thickness.

In a large mixing bowl, add your sliced peaches. Sprinkle with 1/4 cup granulated sugar, 2 tablespoons brown sugar, 1 tablespoon all-purpose flour, 1/2 teaspoon vanilla extract, 1/4 teaspoon ground cinnamon, 1/8 teaspoon ground nutmeg, and 1 tablespoon fresh lemon juice.

Using a gentle folding motion (not stirring), toss the peach mixture 8 to 10 times until all peaches are evenly coated with the sugar and spice mixture. The peaches should glisten and release some of their juice. This step takes about 2 minutes. Checkpoint: Peaches look wet and shiny; sugar is dissolved into a light syrup at the bottom of the bowl.

Pour the entire peach mixture into your prepared baking dish, including all the juice that has collected at the bottom of the bowl. Spread the peaches in an even layer using a spoon or spatula. Checkpoint: Peaches fill the dish evenly with no large gaps.

In a separate medium mixing bowl, combine 1 cup old-fashioned rolled oats, 1/2 cup all-purpose flour, 1/3 cup packed brown sugar, 1/4 cup sliced almonds, and 1/4 teaspoon salt. Stir 3 to 4 times with a fork to combine the dry ingredients. This takes about 1 minute.

Cut 1/3 cup cold unsalted butter into small 1/4-inch cubes. Add the butter cubes to the oat mixture all at once.

Using just your fingertips (not your whole hand), gently rub the butter into the dry ingredients by pinching and working small amounts between your thumb and fingers. Work for 3 to 5 minutes until the mixture looks like coarse breadcrumbs with pea-sized and walnut-sized pieces of butter still visible throughout. The mixture should not be paste-like or smooth. Checkpoint: When you squeeze a small amount, it holds together briefly but crumbles apart easily.

Add 1/4 teaspoon vanilla extract to the topping mixture and stir gently with a fork for about 30 seconds until just combined.

Sprinkle the crisp topping evenly over the peach filling in the baking dish. Use the back of a spoon to spread it into an even layer, but do not press down hard. The topping should look loose and crumbly, not packed tight. Checkpoint: You can still see gaps of peach filling between the topping; topping is about 1/2 inch thick.

Place the baking dish on the middle rack of your preheated 350°F oven. Set a timer for 35 to 40 minutes.

Bake for 35 to 40 minutes until the topping is golden brown on top and the peach filling bubbles visibly around the edges of the baking dish. The filling should bubble for at least 1 to 2 minutes before you remove it. If the topping isn't golden enough after 35 minutes, bake for another 3 to 5 minutes. Checkpoint: Topping is golden to light brown; peach filling visibly bubbles at the edges; you can smell cinnamon and caramelized peach aroma.

Carefully remove the baking dish from the oven using oven mitts. Place it on a wire cooling rack or heat-safe surface. Let the crisp cool for 10 to 15 minutes at room temperature before serving. This resting time allows the filling to set slightly so it holds together better when plated. Checkpoint: You can carefully insert a spoon into the filling without it running all over the plate.

Serve warm in individual bowls. Add a scoop of vanilla ice cream on top if desired, or serve with whipped cream or Greek yogurt on the side. The crisp is best enjoyed within 2 to 3 hours of baking while the topping is still crispy.