Preheat the oven to 350 degrees. Spray a 9x13 inch baking pan with nonstick spray or line with parchment paper.
In an electric mixer, beat 3/4 cup softened butter and granulated sugar on medium speed for 1 minute until fluffy. Scrape the bowl, then add eggs one at a time, mixing until just combined after each. Mix in 2 teaspoons vanilla extract.
In a separate bowl, whisk together gluten-free flour, baking powder, and salt. Gradually add dry ingredients to wet ingredients in two batches, mixing on low speed until just combined.
Scoop the sticky dough into the prepared pan and spread into an even layer. Bake for 20-24 minutes until light golden brown, rotating halfway. Cool completely.
For the frosting, beat 1 cup softened butter on medium-high speed for 1 minute until pale and creamy. Scrape the bowl.
Add powdered sugar, milk, vanilla extract, and salt to the butter. Mix on low until mostly wet, then beat on medium speed for 2 minutes, scraping halfway through. Add gel food coloring if desired and beat to combine.
Spread the frosting onto the cooled bars. Top with gluten-free sprinkles.
Let the bars sit uncovered for an hour to allow the frosting to set before slicing and serving. Store covered on the countertop for 2-3 days or in the refrigerator for up to 5 days.