In the bowl of an electric mixer, beat the butter and both sugars together on high speed for about 3 minutes until the mixture is light, fluffy, and a lovely café au lait color. Scrape down the sides and bottom of the bowl as needed.

Incorporate the vanilla extract and eggs, beating for an additional 2 minutes until well combined. Scrape down the sides again to ensure everything is mixed thoroughly.

Add the salt and baking soda, mixing briefly until evenly combined.

Gradually incorporate the flour and both types of chocolate on low speed until the flour is fully blended and the chocolate is evenly distributed throughout the dough.

Cover the bowl with plastic wrap or transfer the dough to an airtight container. Let it rest in the refrigerator until firm, which may take several hours. If short on time, shape the dough into balls on the baking sheet, chill for about 30 minutes, then proceed to bake.

Preheat the oven to 350°F (175°C) and set a rack in the middle position. Line a baking sheet with parchment paper.

Drop firm, packed 1.5-tablespoon balls of dough onto the prepared baking sheet, spacing them about 2 inches apart. Bake for 11 to 13 minutes, until the edges are golden brown but the centers are still soft and pale. Allow to cool on the baking sheet for a few minutes before transferring to a wire rack.

Continue baking the remaining cookie dough. The cookies can be stored in an airtight container at room temperature for up to 3 days.