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Preheat oven to 300F degrees. Sift together almond flour and powdered sugar; removing the larger lumps of almond pieces. Discard those, you want a really fine powder mixture to create a smooth and pretty top to your cookie.
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Beat egg whites until foamy, then add salt, cream of tartar and white sugar for 6-10 mins. Whip until they form a peak that stands upright. Then add the food coloring.
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Fold flour/sugar mixture into the egg white mixture. Be careful, if you under mix your macaroons they will be lumpy and cracked when they bake and they won't have feet. If you over mix, your macaroons will be flat and won't have feet (the mark of a well-made macaroon). A good measure is 65-75 turns of your spatula when folding.
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Transfer batter to a pastry bag. Pipe out 1 inch rounds on a baking sheet lined with parchment paper. Tap the pan hard at least 2-3 times to release the air bubbles. This will prevent the tops of your macaroons from cracking. Let them sit out for 20-30 mins, or even up to an hour if you want. This will allow them time to dry out a bit. They should be "tacky" to the touch, but not stick to your fingertips. This is another important step to assuring your macarons develop feet! When they dry out they can't spread out in the oven, and are forced to rise up, which is what creates the feet!
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Bake for 20 mins. Whatever you do: DO NOT UNDER BAKE, even if they look done! Otherwise they will stick to your tray. You will also want to avoid opening the oven door while baking.
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Meanwhile mix the buttercream: In the bowl of a stand mixer, beat softened butter for 2 minutes. Add pumpkin pie spice and vanilla extract and slow add powdered sugar until you reach your desired consistency. Add pumpkin puree and beat until fully incorporated. Add more powdered sugar as needed. Transfer to a pastry bag, fitted with a small tip (about ¼ " in diameter)
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Reverse cookie shells on their backs, and pipe a small mound of filling on one of them. Top with the other shell and you have your French Macaroon! If not eating right away, keep refrigerated.