Preheat oven to 375°F. Butter a 9x12 baking dish with 1 tablespoon butter.
In a small bowl, whisk together cinnamon, nutmeg, ginger, and cloves. Set aside.
Melt 1 tablespoon butter in a medium pan over medium heat. Add apples, ½ of the spices, 1 tablespoon maple syrup, and lemon juice. Cook, stirring, until apples begin to soften, about 3-5 minutes. Set aside.
In a large mixing bowl, toss oats with remaining ½ of the spices, baking powder, and salt.
In a medium bowl, whisk together milk, remaining 1/3 cup maple syrup, egg, and vanilla extract. Set aside. Pour milk mixture over the oats and stir to thoroughly combine.
In the prepared baking dish, layer ½ the oats mixture, ½ the apples, and ½ the chopped pecans. Top with another layer of each. Melt remaining 1 tablespoon of butter and drizzle it over the top.
Bake on the middle rack for 40-45 minutes, until the oatmeal is set and beginning to turn golden brown on top.
Meanwhile, in a medium bowl, whisk together cream cheese, maple syrup, milk, and vanilla bean paste with a fork until completely smooth.
Serve baked oatmeal warm with vanilla bean maple cream cheese glaze drizzled over the top.
