Melt 1 tablespoon of butter in a small saucepan. Add the shredded bell pepper. Cook over medium-high heat for 5 minutes or until crisp-tender.
Combine the 6 tablespoons softened butter and the pine nuts in a food processor bowl or blender jar. Process until almost smooth. Add the shredded bell pepper, lemon juice, 1/4 teaspoon salt, and pepper. Process until almost smooth. Set aside and keep warm.
Pour a small amount of salted water into a medium saucepan. Bring to a boil. Add the beans. Cook, covered, for 12 minutes; remove the colander with tongs. Add the bell pepper strips to the liquid in the saucepan and cook for 3 minutes; drain.
Put the beans in a serving bowl. Add half the butter mixture; toss to coat. Arrange the pepper strips around the edge. Serve the remaining butter on the side or reserve for another use.