Add flour, sugar, yeast, salt, thyme, garlic and 1/2 teaspoon of basil to the bowl of a stand mixer. Mix gently until combined. With the mixer on low and the dough hook attached, add olive oil, milk, and warm water. Mix on medium-low speed until the dough pulls away from the bowl and forms a ball.
Transfer dough into a greased bowl and cover with a lint-free towel. Place in a warm location until doubled in size, or about 1 hour.
Roll out dough into a rectangle about 12×20-inches in size. Brush with 3 tablespoons of the melted butter. Sprinkle with 1 teaspoon of dried basil, and all the cheese.
Cut into 6 equal strips (going along the long side of the rectangle so your strips are about 12 inches long). Stack strips on top of each other and cut into six stacks. Carefully transfer these squares into a greased 10-inch loaf pan (so that they are standing up). Cover loosely and let rise again for 30-60 minutes.
Preheat oven to 350°F. After it has risen, drizzle remaining 1 tablespoon of melted butter over loaf. Bake for 35 minutes. Tent with foil if the top of the bread is browning too quickly. I covered mine with foil for about the last 10 minutes of baking.