Line 2 baking sheets with parchment. Spread walnuts on one sheet and toast at 350°F (175°C) for 7–8 minutes until fragrant. Cool completely, then chop.
Brown the butter: In a light-colored saucepan over medium heat, cook the butter, stirring, until the milk solids turn deep golden and it smells nutty, 4–6 minutes. Scrape into a large mixing bowl and cool 15 minutes until lukewarm.
Whisk the Dry Ingredients together in a medium bowl: flour, baking soda, baking powder, sea salt, and espresso powder.
Whisk the sugars into the warm browned butter until glossy and combined, 45–60 seconds. Whisk in the egg, egg yolk, vanilla, and molasses until the mixture looks thick and shiny. Let it stand 5 minutes, then whisk again for 20 seconds to help dissolve the sugars.
Add the dry mixture to the bowl and fold with a spatula just until a few flour streaks remain. Fold in 1 1/2 cups chocolate chips and all the chopped walnuts until evenly distributed. The dough will be soft.
Scoop 2-tablespoon mounds (about 40g each) onto the lined sheets, spacing 2 inches apart. Press a few extra chocolate chips on top of each mound. Chill the scooped dough in the fridge for 20–30 minutes to set the edges.
Heat oven to 365°F (185°C). Bake one sheet at a time for 10–12 minutes, until the edges are set and lightly golden while centers look slightly underdone. At the 8-minute mark, rotate the pan and rap it once against the oven rack to encourage light crinkles.
Immediately sprinkle with flaky sea salt if using. Cool on the sheet for 10 minutes, then move cookies to a rack to finish cooling. Repeat with remaining dough.