In a medium saucepan, melt butter. Add garlic and onion and saute until onion is translucent.
In a measuring cup, whisk half and half and cornstarch. Add salt, pepper and dill and whisk in.
Add cornstarch mixture to sauteed onions. Cook over medium heat, stirring constantly, until thick and creamy. Remove from heat and let cool. At this point you can cool the mixture completely, cover and refrigerate until ready to use, even the next day.
Butter a 13" x 9" or 2 quart casserole dish. Set aside.
Preheat oven to 350 degrees F.
In a large mixing bowl, stir together hash browns, cornstarch mixture, sour cream. Season with salt and pepper. The mixture should be thick and creamy. Spread in prepared casserole dish.
Top with cheese. Bake in oven for 30 to 35 minutes OR until bubbly and cheese is melted.
Remove from oven and cool for 10 minutes.
Garnish with chopped parsley, if desired, and serve.