Preheat oven to 350 degrees. Coat bottom and side of a 9-inch round cake pan with 2 tablespoons butter; sprinkle bottom with brown sugar. In a medium bowl, toss apples with lemon juice; arrange in prepared pan in two concentric circles (you might not use all of them).
In a medium bowl, whisk together the flour, baking powder, salt, and cinnamon; set aside.
With an electric mixer, beat remaining 8 tablespoons butter with granulated sugar until light and fluffy. Add eggs and vanilla; beat until incorporated. With mixer on low speed, alternately add the flour mixture in three parts and the milk in two, beginning and ending with flour mixture.
Spoon batter over apples in pan; smooth top. Bake until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Cool cake in pan on a wire rack, at least 30 minutes and up to 6 hours (if cake has risen above rim of pan, simply push back inside rim).
To serve, run a knife around edge of pan, and invert cake onto a rimmed platter.