Add the warm milk, yeast, and one tablespoon of sugar to the bowl of a stand mixer.
Use a small whisk to gently mix the ingredients together. Allow the mixture to sit for about 10 minutes until the yeast bubbles up and becomes foamy.
In a separate large mixing bowl, whisk together the flour, cocoa powder, and salt. Set aside.
Once the yeast is foamy, add the melted butter, sugar, eggs, food coloring, and vanilla extract to the bowl with the yeast. Fit the stand mixer with the paddle attachment and mix the ingredients on medium for about 1-2 minutes until combined.
Add the flour mixture to the stand mixer bowl in two batches and mix on medium until a shaggy dough forms. Replace the paddle attachment with the dough hook and knead the dough for about 7-8 minutes until smooth and elastic. The dough will be slightly tacky.
Shape the dough into a ball, drizzle olive oil around the stand mixer bowl, and place the dough ball back into the bowl. Turn the dough over in the bowl so all sides get coated in oil. Cover the bowl tightly with plastic wrap then place a tea towel on top. Allow the dough to rise for at least an hour in a warm place until it has doubled in size. This could take up to an hour and a half or more depending on the temperature in your home.
Spray a 9 x 13 baking dish with nonstick cooking spray and set it aside. Beat the softened butter in a small bowl until light and creamy, about 1-2 minutes, and set it aside. In a separate small bowl, whisk together the brown sugar, cinnamon, and salt and set it aside.
Once the dough has doubled in size, punch it down with your fist and turn it out onto a generously floured surface. Roll the dough out into a 12 x 16-inch rectangle with a floured rolling pin.
Spread the butter over the dough all the way to the edge. Sprinkle the brown sugar and cinnamon mixture over the butter and use your hands to pat it into the butter. Starting with the long edge of the rectangle, gently roll the dough into a tight log, finishing with the seam on the bottom.
Use a butter knife to score the top of the dough into 12 sections to make cutting easier. If the ends aren't as full as the rest of the log, you can cut them off and discard them. Use a sharp knife or unflavored dental floss to cut the log into 12 rolls.
Place the cinnamon rolls in the prepared baking dish, leaving a little room in between each one, and allow them to rise in a warm spot for an hour until about doubled in size.
Preheat your oven to 350°F. Once the cinnamon rolls have risen, bake them in the preheated oven for 30-35 minutes until golden brown on top.
While the cinnamon rolls are baking, place the cream cheese and butter in a medium mixing bowl and mix with a handheld electric mixer until smooth and creamy, about one minute. Add the powdered sugar and beat until smooth. Add the heavy cream and vanilla and mix until combined. Slather the frosting all over the warm cinnamon rolls and enjoy!