Soak oil or water off sun-dried tomatoes using a paper towel if necessary, and cut into small pieces.
In a saucepan, heat water and yogurt until steaming, stirring occasionally. Let cool for 5 minutes.
In a stand mixer, combine 1½ cup flour, salt, sugar, cheese, herbs, and yeast. Add yogurt mixture and tomatoes. Mix on low setting until smooth.
Add remaining flour ¼ cup at a time, until the dough is sticky. (you may not need all remaining flour)
Knead with dough hook on medium for 5 minutes.
Remove from mixer and put in a lightly oiled bowl, cover with a heavy cloth, and set in a warm place to rise for 1 hour.
Knead a few more times, then shape into a smooth ball or rectangle. Slice an X on top. Cover and let rise next to the warm oven for 10 more minutes.
Bake at 350° for 30 - 40 minutes.