Bring two separate pots of salted water to a boil. In one pot, add the chicken breasts and poach at a gentle simmer for 12-15 minutes until cooked through (internal temperature reaches 165°F). In the other pot, add the peeled and diced potatoes and cook for 10-15 minutes until fork-tender but not falling apart. Once the chicken is cooked, remove it to a cutting board to cool slightly, then shred it into bite-sized pieces. Drain the potatoes and rinse them with cold water to stop the cooking process and help them cool faster—this prevents them from becoming mushy when mixed with the mayo.
In a large mixing bowl, combine the mayo, onion powder, pickled jalapeño, and jalapeño juice. Stir well to create a smooth, evenly seasoned dressing. I prefer to make this while the proteins are cooling so the flavors have time to meld together. Taste and adjust the seasoning with additional salt and pepper as needed—remember that the potatoes and chicken will absorb some of these flavors.
Add the cooled shredded chicken from Step 1, cooled diced potatoes from Step 1, and the frozen mixed vegetables (peas and carrots) to the dressing in the bowl. Gently fold everything together until all ingredients are evenly coated with the creamy dressing. The vegetables can go in straight from the freezer—they'll thaw quickly from the warm potatoes and chicken while also helping to cool the entire salad. Taste one more time and adjust seasoning if needed. Refrigerate for at least 1 hour before serving to allow the flavors to fully develop and the salad to chill completely.