Preheat the oven to 350°F. Lightly butter an 8x8-inch baking dish and set aside.
Peel and slice 6 to 8 peaches, about 3 to 4 pounds total. Place the sliced peaches in a large mixing bowl.
Add 2 teaspoons lemon juice and 1/4 cup sugar. Gently toss to coat the peaches. Let them sit for 15 minutes.
While the peaches rest, prepare the topping. In a medium bowl, combine 3/4 cup packed light brown sugar, 1/2 cup all-purpose flour, 1/2 cup quick-cooking oats, 1 teaspoon cinnamon, and 1 teaspoon nutmeg.
Add 1/2 cup softened unsalted butter to the dry ingredients. Use a fork or your fingers to mix until the mixture becomes crumbly.
Drain any excess liquid from the peaches. Return the peaches to the mixing bowl and stir in 2 tablespoons all-purpose flour, 1 teaspoon vanilla extract, 1/4 teaspoon salt, and 1/4 teaspoon cinnamon.
Transfer the peach mixture to the prepared 8x8-inch baking dish and spread it into an even layer.
Sprinkle the crumb topping evenly over the peaches.
Bake at 350°F for 30 to 35 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.
Let the peach crisp cool for a few minutes before serving. Serve warm or at room temperature with vanilla ice cream, if desired.