Combine all ingredients except for olive oil in a food processor and blend until smooth. With motor running, slowly pour in olive oil. If spread seems too watery, add a bit more bread.
Store leftovers in the refrigerator for up to a week.
Notes
*To toast walnuts, preheat oven to 350 F and lay out nuts on a cookie sheet. Roast for 8-10 minutes, stirring halfway through, until walnuts are fragrant and just begin to brown. **For DIY pomegranate molasses, combine 2 cups pomegranate juice, ¼ cup sugar, and 1 tablespoon lemon juice in a saucepan. Bring to a boil then lower to a high simmer (sauce should be bubbling) for 1½ hours until reduced to a ½ cup. Sauce should be thick and syrupy. Allow to cool completely. Store in the refrigerator for up to 6 months. One tablespoon fig jam and 2 teaspoons balsamic vinegar can be substituted for the pomegranate molasses.
Recipe by The Mostly Vegan at https://www.themostlyvegan.com/classic-muhammara-red-pepper-walnut-spread/