To make the dough: In a measuring cup, combine your warm milk, 1 tablespoon of sugar, and sprinkle the yeast over. Stir to combine and let sit for 5-10 minutes until the yeast has proofed.

In your stand mixer, add your flour, remaining sugar, and salt, Stir to combine. Add your yeast mixture and mix to combine. Then add in your eggs and vegetable oil and mix to combine. Dough may be very sticky and need 1-2 tablespoons more flour (you want the dough to be somewhat sticky).

Place the dough in a lightly oiled bowl, turn to grease all sides, cover the bowl, and let the dough rise for 60 minutes, or until it's nearly doubled in bulk.

To fill and shape the buns: Gently deflate the dough, and transfer it to a lightly greased work surface. Roll the dough into a 16" x 21" rectangle.

Spread the dough with the 1/3 cup butter. Mix the rest of the filling ingredients in a mixing bowl. Toss to combine. Sprinkle over the butter, Spread out carefully with your hands if need be.

Starting with a short end, roll the dough into a log and cut it into 12 slices.

Place the buns in a lightly greased 9" x 13" pan. Cover the pan and let the buns rise until they're nearly doubled, about 30 minutes.

While the buns are rising, preheat the oven to 400°F.

Uncover the buns, and bake them until they're golden brown, about 15 minutes. While the buns are baking, make the icing.

To make the icing: In a small bowl, beat together the cream cheese, butter, sugar, vanilla, and lemon juice.

Remove the buns from the oven. Spread the icing on the buns while they're warm.

Serve buns warm, or at room temperature. Wrap in plastic and store at room temperature for a day or so; freeze for longer storage.