In stand mixer bowl, add 1 1/2 cups flour, yeast, sugar and salt; mix well. In saucepan or microwave-safe dish, heat milk, water and shortening to 120-130°F (butter does not need to melt). Add to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Add egg; beat on medium speed for 3 minutes.
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: Combine brown sugar, granulated sugar, and cinnamon; set aside.
Punch down dough. On lightly floured surface, roll to a 15x12-inch rectangle. Spread with softened butter. Sprinkle Filling over dough. Starting with shorter side, roll up tightly. Pinch edge to seal. Cut into 12 slices. Place in greased 13 x 9-inch cake pan. Cover; let rise in warm place until indentation remains after touching.
Preheat oven to 375°F.
Bake for 20 to 25 minutes until golden brown. Remove from pan; cool on wire rack while making glaze.
Make the Glaze: Mix the powdered sugar with the heavy cream and vanilla bean paste until thick and smooth. Add more or less heavy cream to get desired consistency. Spread the glaze over the warm cinnamon rolls.