There are many substitutes for eggs, depending on what function the egg plays in the recipe:
Binding: Flaxseed meal mixed with water is a popular substitute for binding. Applesauce, mashed banana, and chia seeds also work! Leavening: Baking powder mixed with water or oil can replace eggs in some baked goods, like cakes and muffins. Moisture: Mashed banana, yogurt, or applesauce can add moisture to replace eggs. Structure: In some cases, puréed tofu can be used to replace eggs and add structure, especially in vegan quiches or frittatas. The best substitute depends on the recipe. For example, you wouldn't want to use a flaxseed meal in a recipe where you need the egg for moisture, because a flaxseed meal is drying.
The yolks are there to add richness and thickness. The coconut cream will make it plenty rich, so you just need to compensate for the thickening. I'd use more cornstarch. Based on this recipe (https://wildwildwhisk.com/haupia/#recipe), which uses 3T for 1 can of coconut milk, I'd start with 6T of cornstarch--I know there's a little extra milk in the recipe you linked, but the use of coconut cream will make it thicker to begin with.
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Binding: Flaxseed meal mixed with water is a popular substitute for binding. Applesauce, mashed banana, and chia seeds also work!
Leavening: Baking powder mixed with water or oil can replace eggs in some baked goods, like cakes and muffins.
Moisture: Mashed banana, yogurt, or applesauce can add moisture to replace eggs.
Structure: In some cases, puréed tofu can be used to replace eggs and add structure, especially in vegan quiches or frittatas.
The best substitute depends on the recipe. For example, you wouldn't want to use a flaxseed meal in a recipe where you need the egg for moisture, because a flaxseed meal is drying.