Preheat oven to 350°F and coat the bottom of a 9- or 10-inch springform pan or baking dish with butter.
To prepare the apples: Peel, quarter, and core the apples. Use a sharp knife to thinly slice each quarter (hasselback style) without cutting all the way through so that the apple stays intact.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter until creamy, about 1 minute. Add sugar and mix until light and fluffy, about 2 minutes longer.
Add eggs one at a time and beat for 30 seconds on high speed after each addition.
Add vanilla extract, salt, and lemon zest and juice. Beating until just combined.
With the mixer on low, add the flour, baking powder, and salt followed by the milk. Beat until just combined. Don't overmix!
Spread cake batter into prepared pan and smooth the top with a spatula. Arrange apples quarters with sliced side up.
While the cake bakes, make the cinnamon-sugar glaze by melting the butter. Off the heat mix in the sugar and cinnamon. Brush mixture all over cake and apples for the last 10ish minute of baking time.
Bake cake for about 45 minutes total, until lightly browned and a skewer comes out clean.
Transfer to a cooling rack let cake cool a bit before serving.