Put the flour, yeast, sugar, and salt in the bowl of a stand mixer. Add the water and 3 tablespoons of the oil and rosemary and stir until you have a very sticky dough.
Using the dough hook, knead the dough until it is smooth and elastic. It should be slick and firm.
Put the remaining oil in a large bowl, add the dough and roll it around so that it's nice and slick. Cover and let rise for about an hour.
Punch down dough and divide it in half. Put aside one half of the dough to use for more muffins or to make a small slab of focaccia.
On a clean work surface such as a large cutting board or a big sheet of waxed paper on a counter, press the dough into a rectangle about 9 inches in length and 6 inches in height.
Brush the rectangle with sun-dried tomato pesto and sprinkle with shaved Parmesan cheese. Roll into a cylinder as if you were making cinnamon rolls. Have ready 6 muffin cups lined with paper liners or just well greased.
Cut the cylinder into 9 rounds and place 1 round in each of 6 muffin cups. Cut remaining mounds into quarters and stack two quarters on top of each round. Sprinkle with sliced olives and bits of colorful cooked peppers (red, yellow and green). Let rise for 30 minutes.
Preheat oven to 375 degrees F. and bake muffins for about 25 minutes or until they are cooked through. Let cool for 20 minutes then remove from tins.