Salvadoran Quesadilla

Add sugar and vanilla to egg yolks and beat on medium-high speed until very pale and fluffy, about 2 minutes. Reduce speed to medium, add cheese and beat just to combine. Reduce speed to low. Add milk in 3 additions, incorporating completely after each addition before adding more. With motor running, stream in 1 cup melted butter and beat until combined. Gradually add dry ingredients and beat until combined, about 1 minute. Scrape batter into a large bowl.