Fit the pie dough into a tart pan with a removable bottom. Press the dough into the bottom and sides and trim any excess. Set aside.
Add the almond paste and sugar to the bowl of a food processor and pulse until you have the consistency of sand. Add the flour and room temperature butter and process to a thick paste. Add the eggs, almond extract and applesauce and pulse until smooth. Spread filling in crust and chill while you prepare the apples.
Working with one apple at a time, peel the apple, cut it into quarters, lengthwise and use a paring knife to remove the core and seeds. Then slice the apple into 1/2" slices. Transfer the sliced apple to a large bowl, squeeze the lemon juice over the apples and toss to coat. Continue with the remaining apple slices, tossing to coat with the lemon juice after each addition to prevent browning.
In a large skillet melt 2 tablespoons of the butter. Add the apples and 1 tablespoon of the sugar and saute until the apples just begin to soften and become pliable. Remove from heat and let cool for a few minutes.
Meanwhile melt the remaining tablespoon of butter and set aside.
When apples are cool enough to handle, arrange them in concentric circles, starting with the rim of the tart, working toward the center. As you get closer to the center, use thinner slices of apple to curl into tighter rosettes.
Very lightly brush the apples with the remaining melted butter, sprinkle with the remaining tablespoon of sugar and scatter the sliced almonds over the tart.
Carefully place the tart pan onto a baking sheet (remember the bottom is removable, so use both hands) Bake for 45-50 minutes until apples and crust are browned. Remove from oven and cool at least 30 minutes. Tart can be prepared up to 8 hours ahead. Serve at room temperature.