Combine the warmed milk (110–115°F), warmed water (100–115°F), 1/4 cup melted-and-cooled unsalted butter, 2 tablespoons honey, and 1 packet active dry yeast in the bowl of a stand mixer and whisk gently to combine. Let sit 10 minutes; the surface should look frothy.
Fit the mixer with the dough hook. With the mixer on low–medium speed, add the 2 whisked large eggs, 2 finely minced garlic cloves, 2 tablespoons finely minced fresh rosemary, and 1 teaspoon kosher salt; mix until combined.
Add 2 cups of the bread flour and mix on medium-low until incorporated. Add the remaining 1-1/2 cups bread flour and knead on medium-low for about 4–5 minutes, until the dough is smooth and pulls away from the sides of the bowl. If the dough is still very sticky and not coming together, add up to 1/2 cup more flour, 1–2 tablespoons at a time, until it is manageable.
Remove the dough from the hook, turn it into a lightly oiled bowl, and turn the dough once to coat it with oil. Cover the bowl with plastic wrap or a clean towel and let rest for 15 minutes.
While the dough rests, spray a 9×13-inch baking dish with nonstick cooking spray and lightly oil your work surface.
After the 15-minute rest, gently deflate the dough on the oiled work surface. Divide the dough into 16 equal portions and shape each portion into a smooth ball (pinch the seams underneath and roll the tops on the surface).
Arrange the 16 rolls evenly in the prepared 9×13 pan. Cover the pan loosely with plastic wrap or a clean towel and let the rolls rise in a warm place until almost doubled in size, about 45–60 minutes (longer if your kitchen is cool).
Toward the end of the rising time, preheat the oven to 350°F.
While the rolls are rising (or in the last 10 minutes), prepare the topping: combine 3 tablespoons melted butter, 2 teaspoons minced fresh rosemary, and 1 teaspoon granulated garlic in a small bowl. Reserve the 2 teaspoons kosher salt for finishing.
When the rolls have almost doubled, remove the cover. Brush the tops evenly with the butter–rosemary–garlic mixture, then sprinkle the reserved 2 teaspoons kosher salt evenly over the brushed tops.
Bake the rolls at 350°F for 20–25 minutes, or until the crust is a deep golden brown and an instant-read thermometer inserted into the center of a roll reads about 190°F.
Remove the pan from the oven and transfer the rolls to a wire rack to cool. Store completely cooled rolls at room temperature for up to 5 days.