1 medium carrot, peeled and thinly sliced crosswise
12 ounces dried soba or udon noodles
3 teaspoons toasted sesame oil
18 sprigs fresh cilantro, long stems removed
2/3 cup natural peanut butter (no added sugar)
1/4 cup plus 2 tablespoons soy sauce
3 tablespoons packed, peeled, and finely chopped fresh ginger (from about a 3-inch piece)
2 tablespoons plus 2 teaspoons fish sauce
2 tablespoons plus 2 teaspoons freshly squeezed lime juice (from about 2 limes)
2 tablespoons plus 2 teaspoons granulated sugar
2 medium garlic cloves, peeled and smashed
1 jalapeño, stemmed and coarsely chopped
2 medium scallions, thinly sliced (white and light green parts only)
1 medium red bell pepper, cored, seeded, and sliced into 1/2-inch strips
1/2 medium English cucumber, thinly sliced crosswise