Possible to thicken gravy without flour or cornstarch

Boil the broth down more before adding the cornstarch.

The broth will continue to thicken as it cools, so aim for a little thin/runny in the pan so it's the right consistency on the table.

Don't be afraid to mix in the cornstarch in multiple, smaller batches.

Edit: For gravy, I prefer the taste of flour to corn starch.

Compared to corn starch, arrowroot:

• Results in a clearer, shinier texture;
• Survives the freezing process much better; and
• Works better in acidic liquids (certain sauces, soups, etc.)

Where it doesn't work so well is in many fruit pies and some other baked goods (because it tends to break down under high heat), and in dairy dishes (you'll end up with a "gooey" texture).

Use arrowroot in place of corn starch whenever your needs match the above.

P.S. Many people are also allergic to corn, and this is probably one of the most common reasons to use arrowroot. If this applies to you, and you're making a dish that is not suited to arrowroot, tapioca flour/starch is another great thickener and actually thickens better than corn starch.