Preheat the oven to 375F. Line a loaf pan (I used 5''x10'') with parchment paper.
In a large bowl, whisk together flour, baking powder, baking soda, and salt.
In a smaller bowl, mix 1 1/2 cups of whole milk with Greek yogurt.
Pour wet ingredients into the dry ones gradually, using a rubber spatula fold and mix the ingredients together, it will form sticky, thick dough in the end.
In a small bowl, combine softened, drained, and chopped sun-dried tomatoes, minced garlic, parmesan, and mozzarella cheese.
Gently fold the sun-dried tomato mixture into the dough with a rubber spatula.
Transfer the dough into the lined loaf pan, level the top out. Line 3 little branches of rosemary in the center of the bread vertically. Finally, brush the top of the dough with around 2 tbsp of milk.
Bake in the oven for 50 minutes. If the top starts burning up (although, it's not likely to happen), cover with foil and continue baking. Test with a toothpick to make sure the bread has fully cooked. The toothpick should come out clean when you insert it in the center of the bread; if it doesn't bake a little longer.
Remove from the oven and let it cool down inside the loaf pan for 10 minutes before pulling the bread by the edges of parchment paper and letting it cool down on wire rack.
Store covered for 3 days or freeze sliced up for up to 8 weeks.