Let milk stand at room temperature for 30 minutes. Preheat oven to 350 degrees F. In a small bowl combine 3 Tbsp. sugar, 2 tsp. flour, nutmeg and a large pinch of salt.
In a large skillet melt 1 Tbsp. of the butter; add half of the apples (do not overcrowd pan) and sprinkle with half of the sugar mixture. Cook over high heat; shaking and turning occasionally until apples are well brown. Squeeze half of the lemon over the apples, using your fingers to catch any seeds. Transfer to a buttered 9x2-inch quiche dish or deep-dish pie plate. Sprinkle with half of the cheese. Repeat with remaining 1 Tbsp. butter, apples, sugar mixture, and lemon; place atop first apple-cheese layer. Sprinkle with remaining cheese.
For custard, in a large bowl whisk the eggs yolks, 2 Tbsp. sugar, 2 Tbsp. flour, and 1/2 tsp. salt. Whisk in 3/4 cup maple syrup, the melted butter, the 3/4 cup room temperature milk, 1/4 cup whipping cream, and vanilla.
In a separate clean large bowl, whisk the egg whites with a clean whisk until soft mounds form. Whisk in the egg yolk mixture just until blended. Pour over the apples using a spoon to gently move the apples a bit to ensure that the custard is distributed throughout.
Bake for 25 to 30 minutes or until custard is browned, set on top, and jiggles just in the center when gently shaken. Interior temperature when tested with an instant-read thermometer should read 160 degrees F. Remove from oven and set on a wire rack to cool. Serve warm or at room temperature with whipped cream mixed with a little maple syrup. Makes 8 servings.