Rinse rice under cold water until water runs clear; set aside.
Melt butter in large saucepan over medium-high heat. Add onions; sauté until translucent, about 5 minutes. Add rice, 2 1/2 cups water, and 1 1/2 teaspoons salt; bring to boil. Reduce heat to low, cover, and cook until rice is tender, about 15 minutes. Remove from heat and let stand, covered, 10 minutes.
Stir in herbs, cherries, & walnuts. Season with pepper and more salt, if desired. Transfer to bowl and serve.