Cream butter and sugar in a large bowl. Add remaining ingredients EXCEPT 1/4 cup of the chopped walnuts. Beat well, scraping once, until dough just starts to come together, but with different sized pieces remaining.
Divide dough onto 2 sheets of waxed paper. Roll one part of the divided dough into a log shape, about 2-inches in diameter and then roll the log in half of the remaining nuts, pressing lightly (it won't completely cover the log). Wrap the log with the waxed paper and repeat with remaining dough. Chill logs until firm, about 2 hours.
Heat oven to 325 degrees and line 2 baking sheets with silicone or parchment.
Cut each chilled log into thin rounds (as thin as possible, 1/8-1/4" thick) and place closely together on prepared sheets (they won't spread). Note: If you'd like, you can add any chopped nuts remaining on the waxed papers to top some of the cookie rounds, pressing them in slightly - use these for the sandwich cookie tops.
Bake 13-15 minutes, turning pans once if needed for even cooking, until bottoms are browned. Cool completely on a wire rack.
Make Ganache Filling:
Place chocolate and butter in a glass bowl and heat in microwave 45 seconds. Stir until melted (it will take a bit, but don't heat anymore - it will become smooth). Alternately, use a double boiler on the stove to melt the chocolate and butter together. It should be thick enough to spread, but if not, leave at room temperature for 15-30 minutes for it to thicken.
Spread about 1 teaspoon of filling onto one cookie half and top with another similar-sized cookie. Repeat until all cookies are used.
Melt a few more chocolate chips and use a fork to add a drizzle over the cookies. Let sit (or refrigerate) until set and store in an airtight container for a few days or freeze for longer storage.
Notes
Make Ahead: You can make the cookies completely and then freeze in airtight containers for up to two months.