In a small bowl, combine the warm milk, warm water, honey, and active dry yeast. Let it sit for about 5-10 minutes until it becomes frothy.
In a large mixing bowl, whisk together the olive oil and egg. Once the yeast mixture is frothy, add it to this bowl. Mix well until everything is combined.
In another bowl, combine the all-purpose flour and salt. Gradually add this mixture into the wet ingredients, stirring until a dough begins to form.
Transfer the dough to a floured surface and knead for about 5-7 minutes until the dough is smooth and elastic.
Place the kneaded dough in a greased bowl, cover it with a clean towel, and let it rise in a warm place for about 1 hour or until it has doubled in size.
While the dough is rising, mix the grated fontina cheese, 1/4 cup of finely grated Parmigiano-Reggiano cheese, and basil pesto in a bowl. Set aside.
Once the dough has risen, punch it down gently and transfer it to a floured surface. Roll it out into a rectangle about 1/4 inch thick.
Spread melted butter over the rolled-out dough. Then, sprinkle the cheese and pesto mixture evenly over the surface.
Cut the dough into strips, then stack those strips on top of each other. Cut the stacked strips into squares for easy pulling apart later.
Place the squares into a greased loaf pan, cover it, and let it rise for another 30 minutes.
Preheat your oven to 350°F (175°C). Once the dough has risen, bake it for 25-30 minutes until golden brown.
