To activate the yeast, pour the warm milk (warm but comfortable to touch) into a small bowl, add 1 tablespoon of sugar (from the ½ cup total), and sprinkle the yeast on top. Mix gently, cover with some foil and a tea towel and let it sit for 5–7 minutes until frothy and activated.
In a large bowl, mix together the flour and salt, then set aside. Once the yeast is ready, add it to a mixing bowl along with the remaining sugar, Greek yogurt, softened butter (nearly all melted), eggs, vanilla extract, and the flour mixture.
Stir with a wooden spoon until just combined for about a minute, then let the dough rest for 5 minutes so the flour can absorb the liquid.
After 5 minutes, use your hands to mix the dough until everything is well combined. Lightly flour your work surface, place the dough on top, and sprinkle a little more flour over it. Knead for 5–7 minutes until the dough becomes smooth and elastic, but not dry. If it feels too sticky, add flour a tablespoon at a time until it comes together—aim for slightly sticky, as that’s what makes soft and fluffy cinnamon rolls.
Transfer the dough to a lightly greased bowl (I used olive oil), cover, and let it rise in a warm spot for 30–45 minutes (check notes if you don't have a warm spot in your home), or until doubled in size. (check notes for dough rising tips)
While the dough is rising, prepare the cinnamon filling by mixing together the softened butter, brown sugar, cinnamon, and vanilla. Set aside.
Grease a 9x13-inch baking dish with butter. Once the dough has risen, lightly flour your work surface and rolling pin. Place the dough on the counter, add a bit of flour on top, and roll it into a rectangle. Spread the cinnamon filling evenly over the dough, leaving a small border around the edges.
Starting from the long side, roll the dough tightly into a log. Use unflavored dental floss or thread to cut the log into 8–12 even rolls, each about 2 inches wide. Place the rolls into the prepared baking dish, cover, and let them proof for 25–30 minutes until puffy in a warm area. Meanwhile, preheat the oven to 350°F (175°C).
When the rolls are ready, warm the double cream in the microwave for 15 seconds and pour it evenly over the top.
Bake at 175°C for 22 minutes, then increase the temperature to 190°C and bake for another 5–7 minutes. After 5 minutes, check the rolls—if the tops are golden, you can remove them from the oven.
While the rolls bake, make the frosting by beating the softened cream cheese and butter together until smooth and fluffy. Add the icing sugar and vanilla extract, then beat again until fully combined.
Remove the rolls from the oven and allow them to cool for 10–15 minutes. Then spread the cream cheese frosting generously over the warm rolls and enjoy the soft, fluffy, and perfectly sweet homemade cinnamon rolls.