A surefire way to avoid artificial food dyes is to make your own natural versions. There are tons of different ingredients you can use to make food dyes and plenty of recipes online to suit your specific project’s needs. Here are a few great ideas to get started.
Yellow and Orange Food Coloring
Golden beets and/or turmeric serve nicely as the basis for yellow food coloring. To make, follow these instructions from Studio DIY: Peel and dice the beet, then mix with ¼ cup of water and a teaspoon or two of turmeric. Soften the beets by microwaving the mixture for approximately 30 seconds; blend, strain, and use the resulting liquid as your dye. The juice from pulverized mangoes and saffron are also good options. If you choose saffron, be careful not to overpower other flavors in the dish. If you’re going for a slightly more orange hue, you can’t go wrong with carrot juice.
Here are some videos that explain how:
Make a Red Velvet Cake without Food Coloring:
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One thing to mention about plant-based food coloring is that the color doesn't always last. I'd bought some nice plant-based food dye to make playdough for my niece. The beet-red faded out to a dim orange-ish brown...and of course the purple that I'd used that red to make, no longer looked purple, either. I think the color faded in about 5-7 days. So, if you're making cookies for an event, you might want to make the red ones the day before...