Apricot-Pecan Filling: Combine apricots, water, corn syrup, sugar and cornstarch in a saucepan. Bring to a boil over medium-high heat. Cook about 3 minutes or until thick, stirring constantly. Remove from heat; stir in pecans. Let cool.
Dough: Combine 1 cup flour, sugar, undissolved yeast and salt in a large mixer bowl. Heat water, milk and butter until very warm (120° to 130°F). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Divide dough into 12 equal portions; shape each into a ball. Place on greased, large baking sheet 2 inches apart. Cover; let rest 15 minutes. Make a deep and wide indentation on each ball by pushing outward toward edge, leaving 1/2-inch ridge around outside. Fill with about 1 tablespoon Apricot-Pecan Filling. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Brush dough with Egg Glaze. Bake at 350°F for 20 to 25 minutes or until lightly browned. Remove from sheet; cool on wire rack. Drizzle with Powdered Sugar Glaze.
Egg Glaze: Beat egg white and water together in a small bowl.
Powdered Sugar Glaze: Combine powdered sugar and milk in a small bowl. Stir until smooth.