Preheat the oven to 375°F (190℃) and line a 12-cup muffin pan with muffin liners. Set aside.
In a small bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, use a hand-held mixer on medium speed to cream together the softened butter and sugar until light and fluffy, about 2 minutes. Add the sourdough discard, eggs, vegetable oil, yogurt, lemon zest, poppy seeds, lemon juice, and vanilla extract. Mix until smooth and combined.
Add the dry ingredients into the wet ingredients and mix until no dry spots remain (no need to over-mix!).
Use a spoon or cookie scoop to fill the lined muffin cups about ⅔ full with batter. Bake for 30-32 minutes until lightly golden brown and a toothpick inserted in the center comes out clean. Let cool completely before adding the glaze.
While the muffins are cooling, make the glaze. In a medium bowl, combine the confectioner's sugar, lemon juice, and milk. Whisk until smooth and combined. Drizzle the glaze over the muffins, then serve.
Notes
To make this recipe with active sourdough starter, replace the sourdough discard with active starter (200g). You do not need to change any other ingredients in the recipe. 1 serving = 1 muffin.