Preheat your oven to 375°F (190°C) and line two baking sheets with parchment paper. You should see the oven rack positioned in the center and the baking sheets ready for use.
In a small bowl, whisk together 2 1/4 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon salt until fully combined. Take 1 minute. This mixture should look uniform in color with no lumps visible. Checkpoint: You are ready to move on when the dry ingredients are fully blended.
In a large mixing bowl, combine 1 cup softened unsalted butter, 3/4 cup granulated sugar, and 3/4 cup packed brown sugar. Use an electric mixer on medium speed for about 3 minutes until the mixture is light, fluffy, and pale. It should look like wet sand or soft frosting. Checkpoint: You are ready to move on when the mixture has increased in volume and looks noticeably lighter.
Add 2 large eggs to the butter mixture one at a time, beating well after each addition. Take about 1 minute total. The mixture should be creamy and smooth.
Pour in 2 teaspoons vanilla extract and beat on medium speed for 30 seconds until the vanilla is fully incorporated. The mixture should smell fragrant and look completely combined.
Reduce mixer speed to low. Gradually add the flour mixture from step 2 to the butter mixture, stirring until just combined. Take 2 to 3 minutes. Stop mixing as soon as you see no white streaks of flour remaining. Do not overmix or the cookies will be tough. Checkpoint: You are ready to move on when the dough comes together without visible dry flour.
Fold in 1 3/4 cups semi-sweet chocolate chips and 1/2 cup milk chocolate chunks using a spatula or wooden spoon. Stir for about 1 minute until the chocolate pieces are evenly distributed throughout the dough.
Unwrap 12 to 15 Cadbury Creme Eggs and carefully cut each egg in half lengthwise using a sharp knife. Place the halved eggs on a plate and set aside. The eggs should be at room temperature for easier handling.
Drop a heaping tablespoon of cookie dough onto a prepared baking sheet. You should use about the size of a walnut. Press the dough down slightly with the back of a spoon.
Place one half of a Cadbury Creme Egg piece (cut-side down) into the center of the dough mound. Press it down gently so it sits just below the surface.
Place another heaping tablespoon of dough on top of the egg, completely covering and sealing it. Gently press the two dough portions together with your fingers so they stick. The sealed dough should look like a small ball with no egg visible.
Repeat steps 8–11 with the remaining dough and egg halves, spacing each dough ball about 2 inches apart on the baking sheets. You should fit about 9 to 12 cookies per sheet. Checkpoint: You are ready to move on when all dough balls are on the baking sheets with no visible egg pieces and adequate space between them.
Place the first baking sheet into the preheated 375°F (190°C) oven on the center rack. Bake for 11 to 13 minutes until the edges are lightly golden brown but the centers still look slightly underbaked and soft. The cookies should not be dark. You'll notice the edges pull slightly away from the parchment paper. Checkpoint: You are ready to move on when the edges are golden and the centers are still slightly soft to the touch.
While the first batch bakes, prepare the second baking sheet in the same way so it's ready to go into the oven when the first batch comes out.
Remove the first baking sheet from the oven and let the cookies sit on the hot sheet for exactly 5 minutes. They will continue to bake slightly from residual heat. During this time, the centers will set just enough to hold their shape when moved.
Using a thin spatula, gently transfer the warm cookies to a wire cooling rack. Take care not to squeeze them, as the centers are still soft. Let them cool completely at room temperature for about 20 to 30 minutes. As they cool, the Creme Egg pieces will set slightly.
Once the first batch is cooling, place the second baking sheet into the 375°F (190°C) oven and repeat steps 13–15.
Once all cookies are completely cooled, combine 2 tablespoons cocoa powder and 1 tablespoon powdered sugar in a small sifter or fine-mesh strainer. Lightly dust each cookie with the mixture for a festive, finished appearance. Checkpoint: You are ready to move on when all cookies are fully cooled and dusted.