Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats. Ensure the butter and eggs are at room temperature.

In the bowl of a stand mixer fitted with the paddle attachment (or using a large mixing bowl and a hand mixer), beat the softened butter until creamy (about 1 minute).

Add the granulated sugar to the butter. Beat on medium speed for 3 to 4 minutes until the mixture is light, fluffy, and pale yellow. Scrape down the sides of the bowl as needed.

Beat in the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract until fully combined.

In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt.

With the mixer running on low speed, gradually add the dry ingredients to the wet ingredients. Mix only until just combined. The dough should be soft and shaggy; do not overmix, as this will result in tough cookies.

Remove the bowl from the mixer. Gently fold in the ½ cup of rainbow sprinkles using a rubber spatula until they are evenly distributed throughout the dough. Avoid excessive mixing to prevent the sprinkle colors from bleeding.

For thicker cookies that don't spread as much, cover the dough tightly and chill in the refrigerator for 30 minutes. If you skip chilling, the cookies will spread more. Use a medium cookie scoop (about 1.5 to 2 tablespoons) to portion the dough, rolling them into smooth balls. Place the dough balls two inches apart on the prepared baking sheets.

Bake one sheet at a time in the preheated 350°F (175°C) oven for 9 to 12 minutes. The cookies are done when the edges are set and lightly golden brown, but the centers still look soft and slightly underbaked.

Allow the cookies to cool on the baking sheet for 5 minutes before carefully transferring them to a wire rack to cool completely. Repeat the baking process with the remaining dough.