1 cup California walnuts, in halves and/or large pieces
3 tablespoons powdered sugar
1 cup canola oil
3 tablespoons unsalted butter
1/2 teaspoon ground black pepper
To make the candied walnut butter, bring the water and 2 teaspoons kosher salt to a boil in a medium-sized saucepan. Add the walnuts, return to a boil, and boil for 2 minutes. Drain the walnuts thoroughly, and while they are warm, toss them together in a bowl with the powdered sugar, until the walnuts are coated.
In a clean, dry, medium-sized saucepan, heat canola oil over moderate heat to 350ºF. Add the walnuts and fry them, stirring almost constantly with a skimmer or slotted spoon, for about 2 minutes, or until the walnuts are golden brown; be careful not to let them get too dark. With a skimmer or slotted spoon, lift the nuts from the oil and place them on a sheet of parchment paper or foil to cool.
Transfer the walnuts to a food processor fitted with the metal blade. Add the butter, pepper, and 1 teaspoon kosher salt. Process for a minute or two, until the walnuts are finely ground and blended with the butter, stopping once or twice to scrape down the sides with a rubber spatula. Scrape the candied walnut butter into small bowl, cover with plastic wrap and set aside.