Linguini with Clam Sauce

This is Addie's favorite dish. She awarded me two stickers for being the "bestest cooker ever" after enjoying two bowls of this tonight! :) I guess that equals two thumbs up?

 Beth's Clam Sauce
1 tsp butter
1/4 cup olive oil
4-6 cloves garlic, minced
3/4 cup white wine (or chicken broth)
4 cans Snow's minced clams, with broth reserved from 2 cans
1/2 cup water
1 heaping tbsp cornstarch
1 lb cooked linguini
grated Parmesan cheese

In a saute pan with sides, heat the butter and oil on medium. Add the garlic and saute briefly. Add the wine (or broth) and clam juice (only the juice!) and simmer for 10 minutes. Mix the water and cornstarch in a cup to make a slurry. Slowly add half of the slurry to the simmering pan and stir well. If it's not thick enough for your liking, add more slurry, otherwise, discard the rest of the slurry. Add the clams and mix well. Remove the pan from heat and toss with the hot pasta. Serve with a sprinkle of Parmesan cheese.