Heat oven to 350°. Butter the bottom of a 10-inch round cake pan with 4 tbsp of the butter. Sprinkle with 1/2 cup of the brown sugar and the sea salt.
Heat remaining 2 tbsp cold butter in a large skillet over medium heat. Add apples; sauté 13 to 15 minutes, until tender. Cool.
In a large bowl, whisk flour, pumpkin pie spice, baking powder and salt. In a second large bowl, beat softened butter and remaining 1 cup brown sugar until smooth. Beat in eggs, one at a time, then vanilla. On low speed, beat flour mixture into butter mixture, alternating with half-and-half. Scrape down sides of bowl; beat for 1 minute.
Fan apples over bottom of prepared pan. Spread batter over apples. Bake at 350° for 45 to 50 minutes, until a toothpick inserted in center comes out clean. Cool for 15 minutes.
Run a small knife around edge of pan. Place a serving plate on top of pan and turn plate and pan over together. Carefully remove pan. If any apples remain in pan, place on cake.
Serve warm or at room temperature with whipped cream, if desired.