Combine first 7 ingredients in a large bowl, stirring with a whisk. Add cucumber; toss to coat.
SAUTÉED MISO VARIATION: Omit seeds, honey, and red pepper; decrease miso to 1 1/2 tablespoons. Combine miso, water, vinegar, 1 tablespoon sliced green onions, 1/4 teaspoon black pepper, and 1/8 teaspoon salt. Heat 1 tablespoon sesame oil in a large skillet over medium heat. Add cucumber to pan; sauté 4 minutes. Toss cucumber with juice mixture.
GREEK VARIATION: Omit first 7 ingredients; decrease cucumber to 2 cups. Combine 1 1/2 tablespoons minced red onion, 1 tablespoon chopped parsley, 3/4 teaspoon chopped oregano, 1 tablespoon lemon juice, 1 1/2 teaspoons olive oil, and 1/8 teaspoon salt. Toss with cucumber, 1 cup quartered cherry tomatoes, and 1/2 cup orange bell pepper strips.
SPICY PASTA VARIATION: Increase seeds to 3 tablespoons; add 1 cup thinly sliced green onions and 1/4 teaspoon salt. Combine seeds and remaining ingredients in a large bowl. Cut 1 (9-ounce) package fresh linguine into thirds; cook according to directions. Drain; rinse with cold water. Toss pasta with cucumber mixture.