Heat oven to 425°F. Place 1-1/4 cups (about half) of the piecrust mix (reserve remainder for another recipe) in a medium-size bowl. Add cinnamon; stir with a fork to combine. Add 2 tablespoons ice water and stir until dough comes together in a ball.
Transfer dough to a floured surface; roll out to a 10-inch circle. Drape into a 9-inch fluted tart pan. Fit into bottom, then fold over edge to come halfway up side of pan. Pierce with a fork, and line with nonstick foil. Fill foil with pie weights; bake crust at 425°F for 8 minutes.
While crust bakes, place egg white and salt in a medium-size bowl. Add 1/3 cup of the sugar (1 tablespoon at a time), beating constantly with an electric mixer. Once sugar is added, beat for 1 minute. Stir in almonds and 1 tablespoon flour.
Remove crust from oven and remove foil and weights. Spread almond mixture over bottom of crust. Set aside.
Peel apples, and cut away from cores. Cut pieces into 1/4-inch-thick slices. Toss slices in a large bowl with remaining 2 tablespoons sugar and remaining 2 teaspoons flour. Fan slices in two concentric circles in crust, packing as closely together as possible.
Bake tart at 425°Ffor 30 to 35 minutes, until apples are knife-tender. Meanwhile, melt jelly in microwave, about 20 seconds. Stir until smooth. Brush jelly onto warm tart. Slice and serve.