Put 7 cups water in a large pot with a tight-fitting lid and bring to a boil. Remove from the heat and let rest for a couple minutes. Stir in the tea leaves (or use a tea ball, cheesecloth, or some other mesh contraption), cover, and steep until fragrant and richly colored, 5 to 10 minutes. Strain the “tea broth through a strainer and put the tea in a large saucepan. Discard the tea leaves.
Bring the tea broth to a boil and sprinkle with salt. Stir in the udon. When the broth returns to a boil, add 2 cups of cold water. When the liquid returns to a boil, turn the heat down so that it bubbles gently without overflowing. Cook, stirring occasionally, until the noodles are just tender, usually 5 to 7 minutes, but it could be more depending upon the brand you use. Taste and add more salt, a few grinds of pepper, and the mirin or sugar, if you like, and serve.