Preheat your oven to 350℉ degrees.
In a medium bowl, toss the diced apples with lemon juice, making sure they’re thoroughly coated, to prevent browning.
In a separate bowl, combine the flour, flaxseeds, cinnamon, ginger, baking powder, baking soda, and salt. Mix well, then add the apples, stirring tossing to make cover all the pieces with flour. This will help prevent them from sinking to the bottom of the batter while baking.
Add the non-dairy milk, applesauce, maple syrup, apple cider vinegar, and vanilla, stirring gently to combine. Don’t worry if there are a few lumps; it’s more important not to over-mix.
Transfer the batter to a silicone 9-inch round cake pan with at least 3-inch high sides, or a standard metal pan lined with foil. Spread it out into an even layer and smooth out the top with your spatula.
Bake on the middle rack of your oven for 60 - 75 minutes, until golden brown all over and a toothpick inserted into the center comes out clean. Cool completely before adding icing.
To make the icing, combine the cashews, maple syrup, vanilla, and a tiny pinch of salt, if using. Blend on high speed for 8 – 10 minutes, until completely silky smooth. Add non-dairy milk just a few teaspoons at time if needed to thin it out to a more pourable consistency.
Remove the cooled cake from the pan and place it on a serving plate. Drizzle generously with icing and enjoy right away!