In the bowl of a stand mixer fitted with a dough hook, add water, yeast, and 1 tablespoon of the granulated sugar. Stir together, then let the yeast rise for about 5-10 minutes. In a small bowl, whisk together buttermilk, egg, and oil until well-combined. After 10 minutes, the yeast should look frothy and bubbly. At this point, pour in the buttermilk mixture, remaining sugar, and salt, and stir together for 10-15 seconds.
Pour in 2 cups of the measured flour, and stir on low speed until incorporated. Continue to pour in flour, 1/4 cup at a time, until the dough pulls away from the bowl and bowl starts to look clean. Increase speed to medium and knead for 5 minutes. The dough should be slightly sticky, but not sticky enough to stick to your fingers when touched.
Transfer dough to a greased bowl, cover with plastic wrap, then set aside in a warm place to rise for 1-2 hours, or until dough has doubled in size.
Meanwhile, prepare the filling. In a small bowl, mix together brown sugar, cinnamon, and cornstarch until combined.
Butter an 11x15 inch glass baking dish, then line with parchment paper, and butter again.
Once dough has risen, liberally flour a large, clean work surface. Punch down the dough to remove air bubbles, then transfer it to the work surface. Roll the dough out into a large rectangle, roughly 20x30 inches wide. Spread softened butter over the surface of the dough, leaving a 1-inch strip on the edge of the dough farthest from you untouched. Evenly sprinkle cinnamon sugar mixture over the butter, then use a rolling pin to gently roll over the mixture and slightly press it into the butter.
Starting with the edge of the dough closest to you, gently roll up the dough into a tight log, sealing it with the strip of dough you left untouched. Cut off any uneven ends. Score dough every two inches, then use those marks to evenly slice your dough into rolls.
Place rolls into parchment paper lined baking dish. Cover with plastic wrap, then set aside in a warm place to rise 1-2 hours, or until rolls have doubled in size and are almost touching each other. Bake in preheated 350 degree oven for 15-17 minutes, or until tops start to brown.
While rolls are baking, prepare your frosting. In a bowl, using an electric hand mixer, beat together butter and cream cheese until smooth and creamy. Add vanilla and lemon juice and beat until combined. Pour in powdered sugar and mix on low speed just until incorporated. Then, increase speed to high and beat for an additional 5 minutes, or until frosting turns white.
Once you remove the rolls from the oven, spread half of the frosting on top of them. This layer will melt into the rolls. Once they've cooled down, spread on the remaining frosting. Serve warm or reheat before serving.