In a small microwave-safe bowl, heat the coconut oil (if using solid) for 10 seconds - that's it. It only takes about 10 seconds to liquify. It should NOT be hot. Just liquid form and tepid.
In a large mixing bowl, beat the butter, coconut oil, and sugars until combined.
Beat in eggs and extracts.
In a large bowl, whisk together flour, baking soda, and cream of tartar.
Gradually add flour mixture to the mixing bowl, 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. The rounder you drop the dough, the taller and puffier the cookie! This helps them also have softer texture, and then there's less crispier 'edge'!
Bake at 375 for 8-11 minutes, or until edges and bottoms are lightly browned.
Remove to wire racks to cool.