Mix 1 tablespoon of the butter with the cornstarch and set aside.
In a saucepan set over medium heat, melt the remaining 3 tablespoons butter. Add the garlic, and cook until the garlic begins to soften, 2 to 3 minutes.
Add the peas and ¼ teaspoon each of salt and pepper, and cook the peas until they turn bright green, about 1 minute.
Add the half-and half and cook until it bubbles in the center, about 30 seconds.
Add the cornstarch mixture and cook, stirring until the content of the pan thickens and the peas are tender.
Add the lemon zest, parsley and tarragon. Taste for salt and pepper, and adjust if necessary. Serve immediately.