Preheat oven to 350 degrees F (175 degrees C). Grease a muffin tin.
Combine pumpkin puree, 1 cup sugar, 1/2 cup plus 2 tablespoons vegetable oil, and eggs in a bowl.
Combine 1 1/2 cups flour, pumpkin pie spice, salt, baking soda, nutmeg, and 1/2 teaspoon cinnamon in a large bowl. Make a well in the center of the mixture; pour pumpkin mixture in and mix thoroughly. Add about 1 tablespoon batter to each muffin cup.
Mix 1/2 cup sugar, 5 tablespoons flour, and 1 teaspoon cinnamon together in a separate bowl. Cut in cold butter with 2 knives or pastry blender until crumb mixture resembles small peas.
Beat cream cheese, 1/4 cup sugar, and 2 tablespoons flour together in a bowl using an electric mixer until creamy. Add 1 tablespoon of cheesecake filling to each muffin cup. Pour in batter until muffin cups are 3/4-full. Top with crumb mixture.
Bake in the preheated oven until tops spring back when lightly pressed, 18 to 20 minutes.