Make the Bread dough: Combine flour, salt and yeast in a mixing bowl or the bowl of your stand mixer. Mix well to combine. Add the butter and mix until well combined.
Next add the warm milk and knwead until a soft dough forms. Cover and rest the dough rise for 1½-2½ hours or until doubled in volume.
Prepare the Filling: Heat 1tsp oil and saute onions for 3~4 minutes. Remove into a bowl. In the same pan, heat 1tsp oil and saute peppers and tomatoes until crisp tender, about 3~4 minutes. Add this to the same bowl. Season with salt. Mix well and set aside.
Punch the dough down and roll it out into a circular disc. Sprinkle the prepared onion-pepper filling, followed by cubed cheese, ground pepper and dried thyme.
Fold the dough over the filling and knead well to incorporate the filling evenly in the dough. Dough is very sticky due to the moisture from the filling, so work with it gently. Form the dough into a log and place it in a greased bundt pan. Pinch the ends close.
Cover the pan and let rise for 1hour.
Preheat the oven to 400°F. Bake the Kugelhopf for 35-40 minutes or until bread is baked and sounds hollow when knocked on.