Place yeast, 1 cup of the warm water, and the sugar in a large mixing bowl that will fit a mixer equipped with a dough hook. Let the mixture sit for about 10 minutes, until the yeast is foamy. Add the remaining ¾ cup of warm water and the milk.
Mix on low speed for about 2 minutes. Add ¾ cup of the olive oil and mix for 1 minute.
Gradually add the flour, giving it a chance to incorporate into the mixture. Mix in the salt.
Transfer dough to a large greased bowl and cover with a damp dish towel.
Let the dough rise in a warm place for 1 ½ hours, or until the dough has doubled in size. Sprinkle cornmeal on a 12 x 16-inch rimmed baking sheet (or a similarly sized pan). Punch down the dough, then spread on the prepared baking sheet. Rub olive oil on your hands before pressing the dough into the pan (this will prevent the dough from sticking to you). Let the dough rest (uncovered) for an additional 30 minutes.
Meanwhile, preheat oven to 425 degrees F.
Use your finger tips to make indentations on top of the raised dough. Drizzle the remaining ½ cup of olive oil over top, using your fingers to spread the oil all over the top of the bread (especially in those little dimples). Sprinkle additional kosher salt, pepper and fresh rosemary on top. Bake until golden brown (about 25 minutes).
Notes
Make sure that your "warm water" is about 100-110°F. If it's too cool, the water will not activate the yeast. Anything hotter than about 130 degrees F will kill the yeast. I use a thermometer to be sure that I'm in the right temperature range, but you're looking for water that feels like a warm bath (not too hot and not too cold).
Focaccia gets a lot of its flavor from all of that olive oil, so it's important to use a high-quality olive oil that actually tastes good. I recommend a really nice extra-virgin olive oil.
If you can, it's best to wait to slice the focaccia until the bread has cooled some. If you slice it straight from the oven, steam will escape and the bread will dry out a bit. Not a disaster (it won't ruin your bread), but something to keep in mind if you can be patient.
Don't have a stand mixer? You can stir the dough together with a spatula or wooden spoon, and then knead the dough by hand for a few minutes on a floured surface.