Before you juice the lemons, zest them and set aside the lemon zest.
Then, add the oat milk and lemon juice to a mixing bowl and let sit about 5 minutes until curdled. This makes a vegan "buttermilk".
Once the milk has curdled, add the organic sugar, applesauce, olive oil, lemon zest, and optional lemon paste to the mixing bowl. Gently mix to combine.
Next, add in the flour, poppy seeds, baking powder, baking soda, and salt. Make sure to add the flour first and pile the other ingredients on top. Then, use a fork to gently mix the baking powder, baking soda, poppy seeds, and salt into the flour to sift together. Finally, mix everything together JUST until a thick batter forms and all streaks of flour are gone. It's important not to over-mix the batter and it's okay if the batter is lumpy- that's actually ideal for these muffins.
Fill a muffin pan with 6-8 cupcake liners and fill each liner with batter until ⅞ full, but not overflowing. Since the muffins will rise and may spread to the sides a bit, it's also a good idea to rub butter or oil along the top of the muffin pan for easier removal. Then, let the muffin batter rest for 30 minutes before baking. While letting the batter rest isn’t 100% necessary, it will allow the batter to rise more. If you want to skip this step the muffins will still taste great, but not rise as high in the oven.
Towards the end of letting the batter rest, preheat the oven to 375F. Then, add the muffins to the middle rack in the oven and bake for 15-17 minutes until cooked through. Try not to open the oven door to check on the muffins or they may deflate and just check them with an oven light.
Remove the muffins from the oven and let cool in the baking tray for 5 minutes. Then, remove and let cool completely on a wire rack. If the muffins are sticking to the baking tray at all, gently run a knife along the edges to help remove. Do not let them cool completely in the pan or they will overcook and risk turning dry.
While the muffins are cooling, make the lemon glaze. Add the sifted powdered sugar, lemon juice, and lemon zest to a bowl and use a fork to whisk together until a thick glaze forms. Drizzle the glaze on top of the cooled muffins. Let the glaze sit for 5 minutes to give it time to set and harden, then serve and enjoy!