In a medium saucepan, bring 1 inch of water to a low simmer. Place 4 ounces unsweetened chocolate and 5 ounces bittersweet chocolate and butter in a heatproof bowl over the saucepan without the water touching from the bottom of the bowl. Stir frequently until the mixture is fully melted. Remove from heat and stir in the vanilla extract. Chill in the refrigerator for 30 minutes.
In a stand mixer fitted with the whisk attachment, on medium speed, beat the sugar and eggs until pale and fluffy, about 5 minutes. On low speed, drizzle in the chocolate mixture for about 15 seconds. The mixture will not be fully combined.
In a medium bowl, combine the flour, baking soda, cream of tartar, salt, espresso powder, the remaining unsweetened & bittersweet chocolate and walnuts. Fold the dry ingredients into the wet ingredients until just combined. Chill the dough in the refrigerator for 3 hours up to overnight.
Preheat the oven to 350 degrees F. Line a sheet pan with parchment.
Drop the dough by the scant 1/4-cup-full. Bake the cookies until they are set in the center, but still a bit soft, about 15 minutes. Cool on the sheet pan for 10-15 minutes before transferring to a wire rack to cool completely.