Spread the walnuts out on a baking sheet and toast them while the oven is pre-heating. They are ready when starting to turn golden and very fragrant, about 10 minutes. Transfer to a cutting board, roughly chop, and set aside.
Place the eggs in a bowl and cover with hot tap water to warm them up. Whisk together the flour, cocoa powder, baking powder, and salt, and set aside.
Melt the chocolate in a double broiler or in a heat-proof metal bowl placed over simmering water. Stir occasionally until melted, then set aside.
Beat the butter and sugar on in a stand mixer or with a hand mixer on medium speed until light and fluffy. Beat in the warmed eggs one at a time until fully combined. Increase the mixer speed to medium-high and beat for 4 minutes. The mixture will gain some volume during this time and become very creamy. Scrape down the sides of the bowl and mix in the melted chocolate and vanilla.
With the mixer on low speed, add the flour mixture. Mix just until the flour is barely incorporated. Using a spatula, gently fold in the walnuts and until evenly distributed. The batter at this point should be glossy and thick.
Line two baking sheets with parchment (do not use Silpats or other baking mats for this recipe; the cookies will stick). Drop rounded tablespoons of batter onto the baking sheets, spaced about 2 inches apart. If you don't use up all the batter in one round, leave it out at room temperature while the first batch bakes — refrigerating makes the batter stiffer and less easy to work with.
Bake the cookies until crackled on top, set around the edges, but still soft in the middle, 14 minutes. Let them cool on the baking sheet for 5 minutes, then carefully transfer them to wire racks to finish cooling using a thin spatula.
Cookies can be kept in an airtight container for about 2 weeks.