Heat the oven to 375 degrees. Line three large cookie sheets with parchment paper.
Coarsely chop the chocolate into half-inch chunks, leaving all the flaky bits on the cutting board. Whisk the flour, baking soda and salt in a medium bowl.
Beat the butter and both sugars with a stand mixer fitted with the paddle attachment on medium speed, scraping the bowl occasionally, until smooth and creamy but not fluffy, about three minutes. With the machine running on medium speed, pour in the cream in a steady stream and beat until smooth. Scrape the bowl, turn the machine to medium-low speed, and add the eggs one at a time, then the vanilla. Beat just until smooth and scrape the bowl.
Turn the machine to low speed and gradually add the flour mixture then the oats. Scrape the bowl, add the walnuts and mix on low speed until evenly incorporated. You should hear the nuts cracking into smaller pieces as the paddle turns. Scrape in all the chocolate chunks and bits and beat on low speed until well mixed.
Use a large (3 tablespoon) cookie scoop to drop balls of dough onto a prepared sheet, spacing them 2 inches apart. Bake until golden brown, about 15 minutes. Scoop the remaining dough while the first batch bakes, then bake the remaining sheets, one at a time.
Cool on the pan on a wire rack.