In stand mixer bowl, add 1 cups flour, yeast, sugar and salt; mix well. In saucepan or microwave-safe dish, heat milk, water and butter to 120-130°F (butter does not need to melt). Add to flour mixture. Using a paddle attachment, beat on medium speed for 4 minutes. Add egg; beat 1 minute.
Switch to dough hook attachment. Gradually stir in enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 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.
For all fillings except Apricot: Combine all ingredients; mix until smooth with mixer or blender. For Apricot filling: In small covered saucepan, simmer apricots in orange juice until tender, 35 to 45 minutes. Drain apricots; discard juice. Pour apricots, sugar, and lemon juice into food processor and blend until fairly smooth and of desired consistency. Refrigerate leftovers. Keeps for several days.
Preheat oven to 375°F.
Punch down dough. Divide dough into 12 to 14 equal pieces. Shape each piece into a smooth ball and place on greased or parchment paper covered cookie sheets. Pat dough balls down to flatten slightly. Let rest 10-15 minutes until slightly puffy. Using 2 fingers, make indentations in the center of each ball. Brush edges lightly with egg wash if desired. Spoon 2 teaspoons of filling into each.
Bake for about 15 - 20 minutes or until golden brown. Remove to wire rack to cool. Serve warm or room temperature.