Melt the butter in a medium pot over medium heat. Add leeks, and cook until soft and translucent, about 10 minutes. Season with salt and pepper.
Add spinach, and cook just until wilted, 2 to 3 minutes. Stir in stock, and simmer until spinach is tender but still bright green, about 6 minutes. Add tarragon and peas, and cook 5 minutes.
Puree soup in a blender until smooth. (You may need to work in batches.) Using the back of a rubber spatula, press soup through a coarse sieve set over a bowl. Season soup with salt and pepper. Taste for seasoning, and adjust as needed. Use a glass measure to pour soup into 2-ounce sake or espresso cups, and serve warm.
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