In the bowl of a stand mixer fitted with a dough hook, add water, yeast, and 1 tablespoon of the granulated sugar. Stir together, let the yeast rise for about 5 to 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 to 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. Increase speed to medium and knead for 5 minutes.
Transfer the dough to a greased bowl, cover with plastic wrap, then set aside in a warm place to rise for 1 to 2 hours, or until dough has doubled in size.
Prepare the filling. In a small bowl, mix together the brown sugar, cinnamon, and cornstarch until combined.
Butter an 11x15-inch glass baking dish, then line with parchment paper, and butter again.
Once the dough has risen, liberally flour your 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 the 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 the cinnamon sugar mixture over the butter, then use a rolling pin to gently roll over the mixture and slightly press it into the butter.
Gently roll up the dough into a tight log. Cut off any uneven ends. Evenly slice the dough into 2-inch rolls. Place in parchment paper-lined baking dish. Cover with plastic wrap. Set aside in a warm place to rise 1 to 2 hours, or until rolls have doubled in size. Preheat oven to 180°C (350°F). Bake on convectional heat function for 15 to 17 minutes, or until the tops start to brown.
While rolls are baking, prepare the frosting. In a bowl, using an electric hand mixer, beat together butter and cream cheese until smooth and creamy. Add the vanilla and lemon juice and beat until combined. Pour in the powdered sugar and mix on low speed. Increase speed to high and beat for 5 minutes, or until the 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.