In the bowl of a stand mixer fitted with the dough hook, pour 3/4 cup warm water, 2 1/4 teaspoons rapid-rise yeast, and 1 tablespoon of the 1/2 cup granulated sugar. Stir to combine and let proof 5 minutes, until bubbly and frothy.

Add the remaining granulated sugar to the mixer and stir on low for 15–20 seconds.

In a small bowl, whisk together 1/4 cup buttermilk (room temperature), 1 egg, and 1/3 cup canola (or vegetable) oil until combined. Pour this mixture into the mixer and stir on low another 20 seconds.

Add 2 cups of the 4 1/2–5 cups all-purpose flour and 1 teaspoon salt to the mixer. Stir on low until incorporated.

Add more flour in 1/4-cup increments, mixing after each addition, until the dough pulls away from the sides and bottom of the bowl. You may not need all of the flour — stop when the dough is tacky but no longer sticky to the touch. Once the dough reaches that stage, knead in the mixer for 5 minutes on medium speed.

Remove the dough, lightly grease the mixing bowl, return the dough to the bowl, and cover with plastic wrap and a dish towel. Let rise in a warm, draft-free place 1–2 hours, or until doubled in size.

While the dough rises, combine the filling: in a medium bowl stir together 1 1/4 cups packed light brown sugar, 2 1/2 tablespoons ground cinnamon, and 2 tablespoons cornstarch. Set aside.

After the dough has doubled, punch it down and turn it out onto a well-floured work surface. Lightly flour the top of the dough.

Roll the dough into a 20 x 30-inch rectangle (or as close as possible), turning and lifting it as you roll to prevent sticking. If edges are uneven, trim them to square the rectangle.

Spread 1/2 cup softened butter evenly over the dough, leaving a 1-inch strip of dough along one long edge free of butter.

Evenly spread the brown sugar–cinnamon mixture over the butter, keeping the 1-inch plain strip clear. If filling falls off the edges, use a bench scraper to push it back onto the dough. Lightly press the filling into the butter with a rolling pin or your hands.

Starting at the long edge opposite the 1-inch strip, roll the dough tightly into a log, finishing with the plain 1-inch strip underneath to seal the seam. Trim the uneven ends to even the log.

Score the log every 2 inches, then slice at the scores to make individual rolls (about 2-inch slices). Arrange the rolls in prepared pans (parchment-lined and butter-greased): place 12 rolls in a 9×13-inch pan and the remaining 3 in a loaf pan, or arrange rolls in an 8×8-inch pan leaving the small ends as needed.

Cover the pans with plastic wrap and a dish towel. Let the rolls rise another 1–2 hours, or until they are touching and have nearly doubled. If you are not using rapid-rise yeast, added extra flour, or your kitchen is cool, this second rise may take 3–4 hours.

Preheat the oven to 350°F. Bake the risen rolls 17–20 minutes, or until the tops begin to brown. Watch carefully so they do not overbake.

While the rolls bake, make the frosting: beat 2 ounces room-temperature cream cheese and 1/4 cup softened butter together until smooth. Stir in 1 teaspoon vanilla extract, 1/2 tablespoon corn syrup, and 1 teaspoon fresh lemon juice, scraping the bowl as needed.

Add 1 1/4 cups powdered sugar gradually and mix until incorporated. Then beat on high for about 5 minutes, until the frosting lightens in color and is fluffy. Scrape the sides and mix briefly again.

When the rolls come out of the oven, spread half of the frosting over them so it melts into the warm rolls. After a few more minutes of cooling, spread the remaining frosting on top. Serve warm.