Combine non-dairy milk, Earl Grey tea, and lavender flowers in a small saucepan with a tight-fitting lid. Place over medium-high heat and bring the mixture to a boil. Remove from heat and cover. Allow tea to steep for 7 minutes.
Then, strain the tea mixture through a fine mesh strainer into a large 2-cup measuring cup. Press the tea and lavender flowers with the back of a spoon to extract as much liquid as possible. Add additional non-dairy milk to bring the liquid amount back up to 1 ½ cups, if necessary. Set the hot milk tea aside for 30 minutes to cool. (see note)
Meanwhile, prepare two 8-inch cake pans by greasing them with shortening or pan spray and inserting parchment circles into the bottom. Then, preheat the oven to 350*F.
Into a medium bowl, combine flour, baking powder, baking soda, and salt. Whisk to combine.
In a large bowl, combine the milk tea, sugar, melted non-dairy butter, vinegar, and vanilla extract. Whisk to combine, then add the dry ingredients and whisk to form the batter.
Divide the batter evenly between two prepared 8-inch cake pans. Use a spatula to evenly spread the batter out, then bake in a 350* oven for 27-30 minutes or until a toothpick inserted into the center of the cakes comes out clean.
Allow to cool for 1 hour in the pans. Then, if necessary, loosen the cakes from the perimeter of the pans with a paring knife and turn them out onto a parchment lined baking tray to cool completely before decorating.