While your cookies are baking, you can start preparing your buttercream. Begin by boiling water in a large pot and then reducing it to a simmer.
In a large stainless steel bowl (I prefer using the bowl of my stand mixer), whisk together 5 egg yolks, ⅓ cup + 1 tsp granulated sugar, 2 tsp vanilla extract, and a pinch of salt.
Place the bowl over the simmering water and constantly stir and scrape the sides to prevent the egg yolks from scrambling. Make sure the mixture reaches a temperature of 155F/68C to ensure the yolks are fully cooked.
Once ready, transfer the bowl to your stand mixer fitted with the whisk attachment. Whisk at high speed until the mixture becomes light, fluffy, and stiff, which should take about 6-8 minutes. If you touch the bottom of the bowl, it should no longer be hot.
With the mixer still running, gradually add your butter and continue whisking until the buttercream becomes thick and creamy.
If you're not using the buttercream immediately, transfer it to an airtight container and refrigerate. You may need to re-whip it before using.