Bring a medium sauce pot of lightly salted water to a boil. Carefully lower the chicken into the boiling water and cook until opaque and cooked through, 5 to 7 minutes. Using a slotted spoon or tongs, transfer to a plate to cool, then using a fork, shred the chicken. Set aside the poaching water for the udon noodles.
While the chicken cooks and cools, prepare the vegetables and almonds.

• Peel the cucumber, if desired, and trim off the ends; cut the cucumber in half lengthwise, then crosswise into ¼-inch-thick half-moons. /li>
• Remove the stem, ribs, and seeds from the bell pepper; thinly slice the pepper.
• Coarsely chop the almonds.

In a large bowl, combine the cucumber, bell pepper, almonds, and Savoy cabbage.

Return the chicken poaching water to a boil. Add the udon noodles and cook until tender, 2 to 3 minutes. Drain and rinse with cold water. Transfer to the bowl with the vegetables. Add the chicken and sesame dressing and toss to coat. Season to taste with salt.
While the water heats and the udon noodles cook, prepare the ginger-scallion sauce.

• Trim the root ends from the scallions; thinly slice the scallions.
• Using the side of a knife, mash enough garlic to a coarse paste to measure ½ teaspoon.
• Grate or peel and finely chop enough ginger to measure 1 teaspoon.

In a small frying pan over medium heat, warm 2 to 3 tablespoons oil until hot but not smoking. Add the scallions, garlic, ginger, and Sichuan peppercorns and cook, stirring occasionally, until the scallions have softened, 4 to 5 minutes. Transfer to a small bowl to cool slightly. Season to taste with salt.

Transfer the chicken noodle salad to individual bowls and top with some of the ginger-scallion sauce. Serve the remaining sauce on the side.