Combine 1 cup flour, sugar, undissolved yeast, salt and coriander in a large bowl. Heat milk, water, 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 eggs, vanilla extract and 1 cup flour. Beat 2 minutes at high speed, scraping bowl occasionally. Stir in pecans, apricots, and remaining flour to make a stiff batter. Turn into well greased 12-cup fluted tube pan. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Bake at 375°F for 30 to 35 minutes or until done. Set pan on wire rack; poke holes in top with cake tester or skewer. Spoon 1/3 of Apricot Glaze over cake. Let stand 15 minutes; repeat. Invert cake on a wire rack; remove pan. Brush with remaining glaze. Cool completely.
Apricot Glaze: Combine apricot nectar and sugar in a small saucepan. Cook over medium-high heat until mixture boils, stirring occasionally. Reduce heat; cook for 5 minutes, stirring occasionally. Remove from stove; stir in rum, if desired. Cool.