In a small saucepan, combine the milk, dill seeds and honey and heat over low heat until warmed. Remove from heat. When the mixture has cooled to 120 degrees F, whisk in the oil and eggs.
In a large bowl, combine 1 1/4 cups flour, yeast, salt and 2 cups of cheese. Add the warm liquid mixture and fresh dill; use an electric mixer to beat for 3 minutes. Add the remaining flour; beat 2 minutes. Scrape down the sides of the bowl. Cover the bowl loosely with a clean dish towel. Let the dough rise in warm draft-free area until doubled, about 1 hour and 15 minutes.
Butter a 9 inch loaf pan.
Do not try to stir or knead the dough. Spoon half of the risen dough into the buttered pan; sprinkle the remaining 1 1/2 cups of cheese over. Add remaining dough to the pan; smooth the top. Cover with a clean dish towel, and let rise in a warm draft-free area until the dough reaches the top of the pan, about 30 minutes. Preheat the oven to 350 degrees F.
Bake until the bread is golden brown, about 45 minutes. Remove the bread from the loaf pan and let it cool on a rack. Slice and serve.