Preheat the oven to 350 degrees F (180 degrees C). Butter a 9x9-inch square pan.
For oatmeal, in a large bowl, whisk together pumpkin, milk, yogurt, olive oil, egg, maple syrup, vanilla, pumpkin pie spice, cinnamon, and salt until thoroughly smooth and combined. Stir in oats and baking powder until incorporated. Pour mixture into the prepared pan.
For cheesecake swirl, beat cream cheese in a bowl with an electric mixer until smooth. Add in ¼ cup yogurt, 2 tablespoons maple syrup, 1 teaspoon vanilla, lemon juice, and pinch of salt and beat until smooth and combined.
Place dollops of cheesecake swirl over pumpkin oatmeal. Use a butter knife to swirl cheesecake in a few times.
Bake in the preheated oven until oatmeal looks set, 40 to 50 minutes. Allow mixture to cool slightly before serving.
