Preheat oven to 350 degrees F (175 degrees C). Line 40 muffin pan cups with paper muffin liners.
Beat eggs, pumpkin puree, and vegetable oil in a large bowl until thoroughly mixed. Stir sugar, baking soda, cream of tartar, salt, cloves, cinnamon, and nutmeg into the egg mixture. Slowly stir matzo cake meal into the batter until combined; pour into prepared muffin cups nearly to the top, as they will not rise much.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 30 minutes.
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