In a large bowl or the bowl of your standing mixer, whisk together the warm water, yeast, and 1 tsp sugar. Set aside to proof for about 10 minutes, or until mixture is foamy.
While the yeast is proofing, add the milk, butter, and remaining sugar to a small saucepan over medium-low heat. Stir frequently, until butter has melted and sugar is mostly dissolved.
When yeast has proofed, add the milk mixture, egg, and salt and stir to combine.
Add the flour about a half-cup at a time, stirring it in with a wooden spoon or the dough hook on your standing mixer, until dough is no longer sticky. You may need a little more or little less flour.
Knead dough by hand on a floured surface or with your dough hook attachment for about five minutes, or until dough is smooth and elastic.
Lightly oil a large bowl with cooking spray. Add the dough to the bowl and turn it to coat. Cover with a damp cloth or saran wrap and let sit in a warm place until it’s doubled in size, 45 minutes to 1 hour.
After dough has risen, punch down and turn onto a clean and lightly floured work surface. Divide the dough into 12 equally sized balls (I start by dividing the dough in half, then each in half again, then each of those into thirds). Roll into balls and tuck the dough in on the bottom to create a smooth top.
Lightly grease a 9x12-inch glass-baking dish with cooking spray. Arrange the balls in the dish so they’re spread out evenly. Cover with a damp cloth or saran wrap and put in a warm place to rise again for 30-45 minutes, until rolls are just touching each other.
Preheat oven to 400 degrees. When rolls are ready, bake in preheated oven for 10-15 minutes, until just the tops are golden brown.
Remove from oven and let cool for about 5 minutes. Serve warm.