Add the warm water, sugar, and yeast to a large mixing bowl or the bowl of a stand mixer.
Let it sit for about 5 minutes, until the yeast begins to look foamy.
Add the sourdough discard, flour, salt, and melted butter.
Mix until everything is well combined and no dry flour remains. If using a stand mixer, mix on low speed for about 3 to 4 minutes.
The dough should be very soft and sticky, but it should still have enough structure to stretch.
Cover the bowl and let the dough rest for 30 minutes.
With damp hands, gently stretch one side of the dough upward and fold it toward the center.
Turn the bowl and repeat on all four sides.
Cover and allow the dough to rise for about 1 ½ to 2 hours, or until noticeably puffy and approximately doubled in size.
Generously grease a 9x13-inch baking pan with the 2 tablespoons butter.
Gently transfer the risen dough to the prepared pan.
Use buttered or damp fingertips to gently stretch the dough toward the edges of the pan.
If the dough springs back, let it rest for 10 to 15 minutes and then stretch it again.
Cover and let rise for another 45 to 75 minutes, until the dough looks light, bubbly, and puffy.
While the dough finishes rising, combine the softened butter, brown sugar, cinnamon, and pinch of salt.
Mix until a thick cinnamon butter paste forms.
Preheat the oven to 425°F.
Once the dough has risen, lightly wet or butter your fingertips.
Press your fingers deeply into the dough to create dimples all across the surface. Be careful not to completely deflate the dough.
Drop small spoonfuls of the cinnamon butter mixture over the dough.
Use your fingertips to gently press some of the cinnamon mixture down into the dimples.
Spread the remaining mixture loosely over the surface.
Bake at 425°F for 22 to 28 minutes, or until the focaccia is puffed, golden brown, and baked through in the center.
If the cinnamon sugar begins browning too quickly, loosely cover the pan with foil during the last few minutes of baking.
Allow the focaccia to cool in the pan for about 10 to 15 minutes before transferring it to a cooling rack.
Let it cool until just slightly warm before adding the glaze.
Whisk together the powdered sugar, 2 tablespoons milk, and vanilla extract.
Add more milk, a small amount at a time, until the glaze reaches your preferred consistency.
Drizzle the glaze generously over the cinnamon roll focaccia.
Slice and serve slightly warm or at room temperature.