Heat oven to 425°F. Lightly grease 6 standard-size cavities of a donut pan.
In a medium bowl with an electric hand mixer on medium speed, beat 2 tablespoons butter, oil, sugar and 3 tablespoons brown sugar until smooth. Beat in egg until just incorporated.
Use a spatula to stir in baking powder, baking soda, nutmeg, 1/4 teaspoon salt and 1/2 teaspoon maple extract until just combined. Stir 1 1/3 cups flour into butter mixture alternately with milk, beginning and ending with flour and making sure mixture is smooth and combined after each addition (batter will be thick).
Spoon or pipe batter into prepared donut pan. Bake donuts 10 to 12 minutes or until a toothpick inserted in thickest part of one donut comes out clean. Cool donuts in pan 5 minutes, then turn out onto cooling rack to cool completely.
Meanwhile, make the crumb topping: In a small saucepan over medium-low heat, melt 3 tablespoons butter. Stir in 1/4 cup brown sugar, 1 teaspoon cinnamon and 1/8 teaspoon salt until combined. Stir in 3/4 cup flour until combined. Continue to cook and stir over medium-low heat 3-5 minutes or until mixture is lightly browned and well combined (mixture will look like wet sand). Remove from heat; set aside to cool.
Make the maple glaze: In a medium bowl, whisk powdered sugar, 1 teaspoon cinnamon, 1 teaspoon maple extract and 2 tablespoons milk until a smooth and slightly drippy glaze forms (add remaining 1-2 tablespoons milk to thin out glaze, if needed).
Dip tops of donuts in glaze; allow some glaze to drip off donuts. Dip glazed donuts in crumb topping, pressing crumbs slightly to adhere to donuts. Return to cooling rack, crumb topping side-up, to set.
If desired, drizzle any excess maple glaze over crumb-topped donuts. Donuts are best served the day they are made, but can be stored in an airtight covered container at room temperature up to 2 days.