Step 1: Prepare the Yeast Mixture. In a small bowl, combine the warm water and dry active yeast. Let it sit for about 5-10 minutes until it becomes frothy.
Step 2: Mix the Wet Ingredients. In a large mixing bowl, whisk together the scalded milk, melted butter or shortening, and 1 1/4 cups of sugar. Allow to cool slightly before adding two eggs and the frothy yeast mixture.
Step 3: Combine Dry Ingredients. In another bowl, whisk together the flour, cornstarch, poppy seeds, and salt. Gradually add to the wet mixture, mixing until just combined.
Step 4: Let It Rise. Cover the bowl with a towel and let the batter rise in a warm place for about 1 hour, or until doubled in size.
Step 5: Prepare the Baking Pan. Preheat your oven to 350°F (175°C). Grease your baking pan, transfer the risen dough to it, and spread evenly.
Step 6: Create the Topping. Combine the remaining egg with a tablespoon of milk and whisk. Brush over the top of the cake before baking.
Step 7: Bake the Cake. Bake for 30-35 minutes, or until golden brown and a toothpick comes out clean.
Step 8: Prepare the Glaze. Mix powdered sugar, lemon juice, melted butter, vanilla, and a pinch of salt. Adjust consistency with more milk if needed.
Step 9: Glaze and Serve. Drizzle the glaze over the cooled cake and let set before slicing.