Line a 13″ x 9″ baking sheet with parchment, and preheat oven to 350 degrees.
Whisk together the flour, loose tea, baking soda and salt in a large bowl.
Place the sugar, nondairy milk, brewed tea, canola oil, vanilla and vinegar in a medium bowl. Stir until combined and the sugar is dissolved.
Pour the liquid mixture into the flour mixture. Stir gently until combined–do not over mix. A few lumps are fine.
Pour into the prepared baking sheet and smooth over the top. bake in the preheated 350 degree oven for 18 to 20 minutes, or until a toothpick inserted in the centre comes out clean.
Remove the cake from the oven and let cool completely. Frost. Cut into slices and serve.