For the soup, in a large stockpot melt the butter with the olive oil; add the onion and sauté until translucent, about 4 minutes. Stir in the carrot, celery, thyme, salt and pepper and cook until the vegetables are tender, stirring frequently, about 3 minutes. Add the corn and stock and bring to a boil.
In a small dish, combine the cornstarch and water to make a paste and whisk in to the boiling soup. Boil for 1 minute. Stir in the cooked noodles and chicken and simmer for 2 minutes. Off heat, add half-and-half or milk and season with additional salt and pepper to taste.
For the Butter Dips, preheat the oven to 425°F. In a large bowl, combine the flour, sugar, baking powder and salt in a large bowl. Use a pastry blender or two knives to cut in the 5 tablespoons butter until the butter is pea-sized. Add the milk and stir until incorporated.
Turn the dough out onto a lightly floured surface and pat into an 8x12 inch rectangle. Slice the dough in half lengthwise, then cut crosswise into 2-inch-wide fingers to make 12 biscuits.
Place the remaining 5 tablespoons butter in a 9x13 baking dish and place in the preheated oven to melt. Remove the pan from the oven and arrange the dough fingers on top of melted butter, side by side. Bake for 20 to 25 minutes or lightly golden and until firm to the touch. Serve warm with soup.