While the crust is cooling, preheat the oven to 325°F (160°C).
Add the sugar and lemon zest to a bowl, and use your fingers to pinch the lemon zest with the sugar. Put the lemon sugar and cornstarch into a saucepan and whisk until combined.
Add the lemon juice and salt to the pan, and heat it over medium heat while whisking occasionally for 2-3 minutes, or until the mixture thickens slightly. Take the pan off the heat.
In a large bowl, add the eggs and yolks and whisk until smooth. While whisking constantly, slowly drizzle in the hot lemon juice mixture ¼ cup at a time.
Once all of the lemon juice has been added to the eggs, pour the mixture back into the saucepan and heat it over medium-low heat and cook while whisking constantly.
When the mixture reaches 175°F (79°C) or is thick enough to coat the back of a spoon, about 5-7 minutes, take the saucepan off the heat.
Place a sieve over a bowl and pass the hot lemon curd through the fine mesh sieve to catch the lemon zest and any hardened bits of egg.
Add the vegan butter 1 tablespoon at a time, mixing after each addition until the lemon curd is smooth and silky.
Pour the lemon curd over the crust and smooth the surface using an offset spatula. Bake the lemon bars for 20-25 minutes, or until the mixture has a slight jiggle when you gently shake the pan.
Let the bars cool completely in the pan (about 2 hours at room temperature) before chilling in the fridge for 1 hour. Lift the bars out of the pan using the parchment paper and use a sharp knife to cut the lemon bars into squares. Wipe the knife clean after each cut.
Optional: dust with powdered sugar before serving.