Place eggs in a saucepan; add water to a depth of 3 inches. Bring to a boil; cover, remove from heat, and let stand 10 minutes.
Meanwhile, combine mayonnaise and next 4 ingredients in a small bowl, whisking until smooth. Stir in celery.
Place eggs under cold running water just until cool enough to handle. Peel eggs; coarsely chop. Fold into mayonnaise mixture. Cover and chill until ready to serve.
Cut each bread slice into 2 triangles. Divide egg salad mixture among bread pieces. Garnish, if desired.