Add ¾ cup unsalted butter, ¾ cup granulated sugar, and ⅓ cup packed light brown sugar to mixing bowl. Beat ingredients together on medium speed until fully incorporated into light, fluffy mixture.
Once creamed, add 1 teaspoon vanilla extract, 1 large egg, and 1 large egg yolk to mixing bowl. Beat ingredients together until just combined.
Add 2 ¼ cups all-purpose flour, ½ teaspoon fresh baking soda, ½ teaspoon fresh baking powder, and ½ teaspoon salt to mixing bowl. Beat ingredients together until combined into thick cookie dough.
Add 1 cup chopped Twix bars and ¾ cup semisweet chocolate chips to cookie dough. Fold candies into dough until thoroughly incorporated.
Cover bowl with plastic wrap and place bowl in refrigerator. Chill cookie dough 1 hour.
Preheat oven to 350° Fahrenheit. Line cookie sheets with parchment paper. Set aside.
Using cookie scoop with release handle, scoop cookie dough out of bowl in 1-tablespoon portions. Roll cookie dough quickly between palms of hands to smooth into ball, then place cookie dough ball on prepred baking sheet.
Repeat process until all cookie dough has been portioned into individual cookie dough balls. Arrange cookie dough balls on baking sheet 2 inches apart.
Place cookie sheets in preheated oven. Bake cookies 6 minutes, then carefully rotate cookie sheets. Bake cookies 6 minutes more or until edges of cookies just begin to brown.
Carefully remove cookie sheets from oven. Immediately place pieces of remaining ½ cup chopped Twix bars on top of warm cookies, then set cookies aside to cool 15 minutes.
After 15 minutes, carefully transfer cookies to wire cooling racks. Let cookies rest until completely cooled, then serve as desired.