Any apple will work in this cobbler, but tart varieties such as Pippin, Granny Smith, or Fuji hold up better in baked desserts and often have more flavor. This is a good basic fruit cobbler recipe that works equally well with peaches, pears, or mangos. It's great on its own, but whipped cream, ice cream, or créme Anglaise make it something special!
Position a rack in the middle of the oven and preheat to 375 degrees F.
Place the apple slices in a large bowl and toss with the lemon juice and salt. Mix together 2/3 cup of the brown sugar and the cornstarch; add to the apples and stir to coat the slices. Transfer the apples to a 9 x 9-inch square baking pan and set aside while you make the topping.
In another medium-size bowl, add the flour, the remaining brown sugar, coconut, baking powder, cinnamon, and allspice, and whisk to blend. Add the butter, and using your fingers, blend it into the dry mixture until the mixture is crumbly. Add half of the beaten egg and stir in with a fork to combine. The remaining beaten egg can be discarded or saved for another use.
Place the topping over the apples, covering the fruit completely (clumps are okay). Bake until the apples are tender when pierced with a knife, the filling bubbles, and the topping turns golden, 30 to 40 minutes. Transfer the pan to a wire rack and cool slightly before serving.