Start with the apples. Peel, core and slice them.
In a large bowl, combine the filling ingredients: apple slices, brown sugar, melted butter, cinnamon, lime/lemon juice and a tablespoon of all-purpose flour.
In a medium bowl, bring together the topping. Start by cutting cold butter into the flour and brown sugar. You can use a fork, a pastry cutter, or even your hands. When all the ingredients are well combined, add the almond slices and stir until evenly distributed. Topping should look sightly sandy, but with some small chunks of butter.
Combine filling and topping. In a large, wide dish, spread the apple mixture equally. Spread the topping, covering completely the apple filling.
Preheat oven to 350°F.
Bake in the middle rack for 40 minutes, or until bubbly and golden brown. Check apples before removing from the oven: you should be able to poke them with a fork and feel them soft and tender.
For the eggnog sauce, in a small saucepan, heat the eggnog, cinnamon and nutmeg over medium-low heat.
Combine the cornstarch and heavy cream and pour into the hot eggnog mixture. Turn the heat to low to avoid boiling and whisk regularly.
When it begins to thicken, whisk constantly, until it reaches an almost pudding-like texture.
Serve apple crisp hot, with eggnog sauce on top.