Soak cashews in very hot water for 1 hour or in cool water for 6-8 hours. Drain thoroughly and add to a blender. To the blender, also add remaining ingredients, depending on which style of frosting you're going for.
Blend until creamy and smooth, scraping down sides as needed. It's important to get the frosting as creamy and smooth as possible, so blend on high with a high-speed blender until the texture is silky and smooth.
Taste and adjust flavor as needed, adding more maple syrup for sweetness, vanilla for vanilla flavor, or (if making the tangy frosting) more apple cider vinegar or lemon zest for tang.
Transfer frosting to a medium mixing bowl (with room to blend / whisk) and cover. Place in the freezer and chill for 45 minutes. Then remove from freezer and whisk. Freeze for another 45 minutes - 1 hour and whisk again. Then leave in the freezer until semi-firm to the touch (cheesecake texture // ~ 2-4 hours) and use a hand mixer (or whisk) to blend until creamy and smooth. Depending on how firm your frosting is, this may take a little work at the beginning as it softens. If too thick, microwave in 15-second increments until blendable (or leave out at room temperature to soften).
Your frosting is ready to use! Or it can be stored in the refrigerator up to 5-7 days (or the freezer 1 month). The nature of this frosting is like most other frostings in that it will soften out of the refrigerator. So, if serving a cake with this frosting, it's best to keep the cake refrigerated. Once ready to serve, it is fine staying out of the refrigerator for several hours.
*If avoiding oil, omit. The frosting should still firm up, but it won’t be as creamy. *Because the recipes are very similar, I included one nutritional information estimate for both. It is a rough estimate for 1 quarter-cup serving calculated with full-fat coconut milk and lesser amount of maple syrup. *Recipe makes ~2 cups frosting.