Place the 2 ounces of baking chocolate and the 2 ounces of dark chocolate in a large saucepan. Add 1/2 cup heavy cream and 2 cups half-and-half. Place over medium heat, and, stirring continuously, bring to a simmer and melt the chocolate.

Whisk together sugar and cocoa in a small bowl.

In the bowl of a stand mixed fitter with the whisk attachment, beat the egg yolks on low. Slowly add the sugar-cocoa mix and continue beating until well-blended, about 30 seconds.

With the mixer still on low, slowly add the hot cream and chocolate mixture. Beat until well mixed, then transfer back to the saucepan.

Heat mixture over medium heat until mixture thickens, small bubbles form near the edge, and everything is steamy.

Remove from heat and stir in the 1 1/2 cups heavy cream, salt, and vanilla. Transfer to a bowl, cover, and chill for at least 8 hours.

Assemble ice cream maker and churn for 10 to 15 minutes, adding chopped dark chocolate during the last 1 to 2 minutes.

Serve, and transfer remaining ice cream to an airtight container and freeze.