Preheat the oven to 400 degrees. Coat a 12-cup muffin tin with cooking spray or line with paper baking cups.
To make the topping, stir together the oats, sugar, and cinnamon in a bowl. Stir in the butter.
To make the batter, combine the flour, oats, baking powder, baking soda, and cinnamon in a large mixing bowl. In a second bowl, mix the applesauce with the milk, vegetable puree, sugar, oil and egg with a wooden spoon. Add the flour mixture slowly, stirring until just moistened. Do not overmix - the batter is supposed to be lumpy.
Divide the batter evenly among the muffin cups and sprinkle with the streusel topping. Bake until the topping is lightly browned and a toothpick comes out clean when inserted into the center of the muffins, 18 to 20 minutes. Turn the muffins out onto a rack and serve warm or cool.