Chocolate Budino With Candied Walnuts

Name: Chocolate Budino With Candied Walnuts
Ingredients: 1/2 cup sugar; 1 cup coarsely chopped walnuts; Kosher salt; 1 cup bittersweet chocolate wafers (disks, pistoles, fèves; preferably 70%–74% cacao) or 5 oz. chocolate, finely chopped; 1 cup heavy cream; 1 cup whole milk; 6 large egg yolks; 1/4 cup sugar; 3/4 tsp. kosher salt; 1 Tbsp. extra-virgin olive oil (preferably Olio Verde), plus more for serving; Flaky sea salt; Freshly ground black pepper; Salted caramel gelato or ice cream (for serving; optional)