Add your warmed milk, water, butter, honey, and yeast to the bowl of an elextric mixer. Gently whisk to combine.
Let sit for 10 minutes. You should notice the mixture looking frothy on top. This shows that the yeast is still fresh and good.
Add the dough hook to the mixer and on medium speed add the whisked eggs, garlic, rosemary, and kosher salt.
Add 2 cups of flour and gently knead on medium-low speed until it is incorporated.
Add in the remaining 1-1/2 cup of flour and knead the bread for 5 minutes until it's smooth in appearance and is fully pulled away from the bowl. If the dough does not seem to be coming together add up to 1/2 cup more flour.
Remove the dough from the bread hook and add back to the bowl. Cover with a towel or plastic wrap for 15 minutes.
While the dough rests, spray a 9x13 baking dish with non-stick cooking spray and lightly oil your work surface. I like to use the non-stick cooking spray to oil my work surface.
Gently deflate your dough and turn it out on the oiled work surface.
Shape the dough into 16 equally sized rolls.
Add rolls to the prepared pan.
Cover the pans and let the rolls rise in a warm place until almost doubled 45-60 minutes. If your house is cooler it will take a longer time for the bread to rise.
Toward the end of the rising time preheat the oven to 350 degrees F.
Brush the top of the rolls with the butter mixture and sprinkle with kosher salt.
Bake the bread for 20-25 minutes, or until its crust is a deep golden brown and a digital thermometer inserted into the center registers about 190 degrees F.
Remove the rolls from the oven, and set them onto a rack to cool. Store completely cool bread at room temperature for up to 5 days.