In a stand mixer bowl, combine 2 cups flour, yeast, sugar and salt; mix well. In saucepan or microwave-safe container, heat milk, water and shortening until warm (120-130°F; shortening does not need to melt). Add milk mixture to flour mixture. Add eggs. Blend at low speed until moistened; beat 3 minutes at medium speed.
Switch to dough hook attachment. Gradually stir in enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 8 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Prepare filling: In medium saucepan, combine brown sugar, evaporated milk, butter and corn syrup. Cook over low heat, stirring occasionally, until sugar has dissolved and butter has melted; set aside.
Punch down dough. Divide into pieces the size of a walnut; shape each piece into a smooth ball. Pour one third of filling into well-greased 12-cup bundt pan. Sprinkle with half of coconut and walnuts/pecans. Place half of the balls in pan. Pour one third of filling over balls; sprinkle with remaining coconut and walnuts/pecans. Add remaining balls; pour remaining filling on top. Cover; let rise in warm place until indentation remains after lightly touching, about 30 minutes.
Preheat oven to 375°F.
Bake for 45 to 50 minutes until golden brown. Cool 10 minutes in pan; invert onto serving plate. Serve warm or cold.