Cook apricots, sugar, and 1 cup water in a small heavy saucepan over low heat, stirring occasionally, until apricots are plump, soft, and just beginning to break down, about 30 minutes. Transfer compote to a small bowl and let cool completely. DO AHEAD: Can be made 1 week ahead. Cover and refrigerate. Preheat oven to 350°F. Combine all ingredients in a large bowl. Rub mixture with your fingertips until butter is completely incorporated and mixture resembles wet sand. Spread out on a rimmed baking sheet. Bake, stirring occasionally, until golden brown, 15-17 minutes. Let cool completely. DO AHEAD: Can be made 3 days ahead. Store airtight at room temperature. Scoop 2 tablespoons ice cream into each small jar or sturdy glass. Spoon 1 tablespoon apricot compote over ice cream and top with 1 tablespoon crumble. Repeat with remaining ingredients for 6 layers total. Freeze for 30 minutes to set.