Butter pan and fit a round of parchment paper in bottom. Butter parchment, then flour pan.
Spread 1/2 stick butter thickly on bottom of a 12-inch heavy skillet and sprinkle 1/2 cup sugar evenly over butter. Arrange apples, cut sides down, over sugar and sprinkle with 1/4 teaspoon salt. Cook over medium heat, turning apples occasionally, until sugar is caramelized and apples are tender and golden brown, 15 to 20 minutes.
Arrange apples, cut sides down, in concentric circles in bottom of cake pan, then pour over any caramel from skillet.
Whisk together flour, baking powder, baking soda, allspice, cinnamon, nutmeg, and remaining 1/2 teaspoon salt.
Pulse walnuts with remaining cup sugar in a food processor until finely ground.
Beat remaining 1 1/2 sticks butter in a bowl with an electric mixer until creamy, about 3 minutes. Add walnut sugar and beat until just combined. Add eggs 1 at a time, beating well after each addition, then beat in extracts. At low speed, mix in flour mixture until just combined (batter will be thick).
Dollop batter over apples and spread evenly. Bake until torte just begins to pull away from side of pan and a wooden pick inserted in center comes out clean, 45 to 50 minutes. Cool torte in pan on a rack 30 minutes. Put rack over torte, then invert torte onto rack.
Melt apple jelly in a small heavy saucepan over low heat, stirring. Brush apples generously with jelly, then cool torte completely, 1 to 1 1/2 hours.