Sprinkle the all-purpose flour over the butter and onion mixture. Use a whisk to combine everything into a thick paste. Continue to cook this roux for 2 to 3 minutes, whisking constantly. This step is essential to cook out the raw flour taste and will give your gravy a beautiful golden color.
Slowly pour in the non-alcoholic apple cider while whisking vigorously to prevent any lumps from forming. Once the cider is fully incorporated, gradually add the chicken or vegetable broth. Continue whisking until the mixture is completely smooth and starts to thicken.
Bring the gravy to a gentle simmer. Reduce the heat to low and let it cook for about 10 minutes, stirring occasionally. The gravy should thicken enough to coat the back of a spoon. Stir in the sea salt, black pepper, and apple cider vinegar. Taste the sauce and adjust the seasoning if needed.
If you prefer a perfectly smooth gravy, pour the mixture through a fine-mesh sieve into a heat-proof container to remove the onion bits. If you enjoy a bit of texture, you can skip this step. Allow the gravy to cool to room temperature before covering it tightly and placing it in the refrigerator.