In a 3- to 4-quart pan, stir nuts often over medium heat until lightly toasted, about 3 minutes; pour from pan.
Turn heat to medium-high and add butter, onion, carrots, garlic, and parsley to pan. Stir often until onion is limp, about 5 minutes.
Add barley and rice. Stir often until barley is lightly browned, about 4 minutes.
Add broth, sherry, basil, and oregano. Bring to a boil over high heat, then turn heat to low, cover, and simmer 30 minutes. Stir in bulgur, cover, and simmer until grains are tender to bite, about 15 minutes longer.
Add salt and pepper to taste. Pour pilaf into a bowl and garnish with toasted nuts.