Begin by filling a medium pot with at least 1-inch of water and bring it to a gentle simmer. This will create a double boiler effect, which is essential for making the meringue.
Thoroughly wash and dry the stainless steel mixing bowl from your stand mixer. It's important to ensure the bowl is grease-free, as any oil can prevent the meringue from whipping up properly.
Add the 7 egg whites and 2 cups sugar to the mixing bowl. Using a whisk, combine the ingredients until mixed.
Place the mixing bowl over the saucepan of simmering water, ensuring the bowl does not touch the water. This gentle heat will help dissolve the sugar while whipping the egg whites.
Whisk constantly for about 3 minutes, or until the mixture reaches 160°F. It's important that the sugar fully dissolves; you should not feel any granules when rubbing the mixture between your fingertips.
Once it reaches temperature, carefully remove the bowl from the heat. Wipe any water from the bottom of the bowl and transfer it to your stand mixer fitted with the whisk attachment.
Beat the mixture on medium-high speed for about 15 to 20 minutes until stiff glossy peaks form. The bottom of the bowl should feel completely cool, as warm meringue will melt the butter later.
Once your meringue is ready and cool, switch to the paddle attachment. Reduce the speed to medium and begin adding the 1 1/2 cups softened unsalted butter, 1 tablespoon at a time, incorporating it gradually.
After all the butter is added, scrape down the sides of the bowl and continue beating for about 3 minutes until it reaches a thick whipped consistency. If it appears lumpy or liquidy, keep beating until it is smooth.
Finally, add the 2 tsp vanilla extract and 1/4 tsp fine sea salt. Mix on medium-high speed until fully incorporated, which should take about 1 minute.