In a medium sauce pan bring water and 1/2 tsp. salt to boil. Slowly stir in polenta, then reduce heat to low and simmer slowly until mixture is very thick, about 30 minutes; stirring frequently to avoid sticking.
Meanwhile, melt butter in a skillet and add 5-6 sprigs of fresh herbs, stems in tack. Gently stir herbs in melted butter for 3-4 minutes, then remove from heat. Remove herbs sprigs and discard.
When polenta is done remove from heat and stir in herb infused butter, 1/2 cup parmesan cheese, salt & pepper to taste. Pour polenta into a well oiled shallow baking dish. Cover with plastic wrap and allow to rest for 10 minutes.
Meanwhile, prepare poached eggs to desired doneness.