Make the dough: Warm the milk, mix in the yeast and sugar, then stir it into the flour to form a rough dough. Let the dough rest briefly, then work in the 3 tablespoons butter and salt and knead until smooth. Shape the dough into a ball, place it in a greased bowl, and let it rise until doubled, about an hour.
In a small pan, melt ½ cup butter and stir in the minced garlic. Set aside.
In a shallow bowl, combine shredded Toma with parsley and chives.
On a lightly floured work surface, press the risen dough into a square, about ½ inch in thickness, and cut it into 36 pieces.
Gently shape each piece into a disk. Dip each dough disk in the garlic butter, then coat lightly in the cheese and herb mixture.
Layer the disks into a well-buttered bundt pan. As you are layering, occasionally sprinkle more cheese between layers of disks, adding more on top, also. Set aside and allow the bread to rise again until slightly puffy, about 30 minutes.
Preheat oven to 350F. Bake bread until golden and cooked through, about 35-40 minutes. Invert onto a serving plate, then invert again, so the browned side is on top. Serve immediately.