1. Preheat oven to 300°F. Spread bread cubes in a flat layer on 2 baking sheets. Toast, stirring often, until dried but not browned, about 20 minutes. Transfer to a bowl; cool completely. Increase oven temperature to 375°F.
2. Melt butter in a large pan over medium-high heat. Add onions and celery; sauté until softened but not browned, 3 to 5 minutes. Add sage, parsley and thyme. Pour in broth, increase heat to high and bring to a boil. Remove from heat; cool slightly.
3. Add eggs to bowl with bread cubes; stir to coat. Pour in broth mixture; stir in apricots and pecans. Season with 1/2 tsp. salt and 3/4 tsp. pepper. Spoon into a greased 3-quart baking dish. (Can be done to this point up to 2 days ahead. Cover and chill. Bring to room temperature before continuing.)
4. Cover with foil; bake for 30 minutes. Remove foil; bake 20 minutes. Let stand for 10 minutes; serve.