Start by preheating your oven to 400°F and lining a baking sheet with parchment paper. Take your puff pastry out of the freezer and let it thaw according to the package directions. I like to keep it in a cool spot rather than a warm kitchen so it doesn't get too soft.
Peel, core, and thinly slice your granny smith apples. In a mixing bowl, combine the sugar, cinnamon, and half of the melted butter, then toss the apple slices through until every piece is coated. Set this bowl aside while you get the pastry ready.
Lay your pastry sheet flat and cut about half an inch in from the edge all the way around, but leave two opposite corners uncut so the border stays connected. Fold one edge over to the opposite side and repeat with the other. This step is optional, but I think it creates a beautifully thick, bakery-style border.
Brush the entire pastry surface with the remaining melted butter, avoiding the folded edge if you did the border technique. Then sprinkle the ground almonds evenly over the middle of the pastry. This little layer is what keeps your finished tart from turning soggy underneath.
Take your coated apple slices and arrange them neatly over the almond layer, slightly overlapping each row so they look tidy once baked. I like fanning them out in even rows for a nicer presentation, though a casual scatter tastes just as good.
Slide the tart into your preheated oven and bake for 30 to 35 minutes, until the pastry is puffed, golden, and crisp underneath. If the bottom hasn't browned yet, give it another five to ten minutes at a slightly lower temperature so it doesn't burn on top.
As soon as the tart comes out, warm the apricot jam in the microwave or a small saucepan until it's loose, then brush it over the warm apples for that glossy finish. Transfer the tart to a wire rack so it cools without getting a soggy bottom from sitting on the baking sheet.