Make the dough: Place the warm water in a large bowl of a large mixing bowl and whisk in the granulated sugar and yeast. Then, whisk in the oil, buttermilk, egg, and salt until combined. Finally, add the flour. Using the dough hook or paddle attachment, or using a silicone spatula and mixing by hand, beat the mixture until a soft dough forms and begins to gather itself into a ball– about 3-5 minutes. If the dough is very sticky, add in 2-4 Tablespoons of flour.
Remove the dough and form into ball on your work surface. Mist the bowl with non-stick spray, then place the dough back in the bowl. Cover it with plastic wrap or a clean towel, and allow it to proof for 1 hour at room temperature.
Once the dough has proofed for about 30 minutes, stir together the brown sugar and cinnamon in a small bowl. Once proofed, use a rolling pin to roll the dough out into a 14x12-inch rectangle, about ⅛-inch thick. Evenly spread the softened butter on top and sprinkle the cinnamon sugar mixture over the buttered dough.
Generously grease a 9-inch deep dish pie dish or a 9-inch round cake pan with butter or nonstick spray.
Using a pizza cutter or sharp knife, cut the dough into about 2-inch wide strips. Roll up on strip and place it in the center of the pan. Then, coil the remaining strips around the center roll, starting each at the end of the previous one to make one large cinnamon roll. (Some of the filling may fall out as you pick up the strips, you can sprinkle it over the cake when finished).
Loosely cover the cake with plastic wrap or a clean towel and allow it to rest in a warm place, for 1 hour or until it doubles in size.
Once it rises, preheat the oven to 350ºF. Bake for 30-35 MINUTES or until golden brown. If the top or edges are browning too quickly, carefully tent the cake with aluminum foil.
Remove the cinnamon roll cake from the oven and allow to cool in the pan for 10 minutes while you make the icing. In a large bowl using the paddle attachment of a stand or hand mixer, beat together the cream cheese and butter. Then, add the vanilla and lemon juice. Finally, add the powdered sugar on low speed, increasing speed to medium until smooth and fluffy. Spread the cream cheese icing over the warm cinnamon roll cake.
Serve warm. The cinnamon roll cake with stay fresh covered tightly in the refrigerator for up to 3 days. Reheat as desired.