To make streusel topping, toast aniseed in a small skillet over medium heat until slightly darker in color, about 3 minutes. Place seeds in processor. Add next 5 ingredients; blend 5 seconds. Add butter; pulse blender until mixture resembles coarse crumbs. Transfer mixture to large bowl. Drizzle egg over and stir until ingredients are evenly moistened.
Preheat oven to 375°F. Combine first 8 ingredients in large bowl; stir to combine. Add apples and lemon juice; toss to blend. Transfer filling to a shallow 2-quart baking dish. Crumble topping finely over filling.
Bake crisp until apples are tender, juices bubble thickly, and topping is crisp and golden, about 1 hour. Cool 15 minutes. Serve warm, with vanilla ice cream or freshly whipped cream.
*Adapted from Bon Appetit