In a large mixing bowl, beat the butter, oil, and sugars until combined.
Beat in eggs, vanilla, and maple extract.
In a large bowl, whisk together flour, baking soda, and cream of tartar.
Gradually add flour mixture to the butter mixture, beating until just combined after each addition. Do not overmix.
Line baking sheets with parchment paper or silicone baking mats.
Drop dough by small teaspoonfuls onto baking sheets.
Bake at 375 for 8-11 minutes, or until edges and bottoms are lightly browned.
Remove to wire racks to cool.
In a medium bowl, whisk together butter, maple syrup, vanilla, maple extract, and 3 cups powdered sugar.
Add additional powdered sugar, as needed, to achieve a consistency that is thicker than a glaze - it shouldn't run off the cookie - but easily spreadable.
Frost cookies, and allow to set.
These are good for at least a week, but best within the first 3 days. After 3 days, they get crumbly and a bit on the drier side - still a delicious cookie though.
These freeze really well! Iced or plain, they freeze beautifully.
I've made these Amish Sugar Cookies into Pumpkin Spice Latte Amish Sugar Cookies, Iced Chai-Spiced Amish Sugar Cookies, Iced Almond Cookies, Iced Lemon Amish Sugar Cookies, Iced Orange Amish Sugar Cookies, Toasted Coconut Amish Sugar Cookies, Coconut Oil Amish Sugar Cookies, and Thin Crispy Amish Sugar Cookies!