In a medium saucepan, combine the diced apples, brown sugar, cinnamon, nutmeg, lemon juice, and vanilla extract. Cook over medium heat for about 5-7 minutes, until apples soften and become syrupy. Let it cool completely.

1. In another saucepan, combine milk, heavy cream, and sugar. Heat over medium until sugar dissolves. In a separate bowl, whisk egg yolks. Gradually add warm milk mixture to egg yolks, stirring constantly. Return to saucepan and cook over low heat until custard thickens and coats the back of a spoon (5-7 minutes). Remove from heat, add vanilla and cinnamon, and cool.
2. Preheat oven to 350°F (175°C). Combine flour, butter, brown sugar, and salt. Mix until it forms crumbs. Spread mixture on a baking sheet and bake for 10-12 minutes, until golden brown and crispy. Let cool.
3. Once both the apple mixture and custard are cooled, combine them. Pour into an ice cream maker and churn until soft-serve consistency (20-25 minutes). Add cooled crumble during last few minutes of churning.
4. Transfer gelato to an airtight container and freeze for at least 3-4 hours or until firm.