Peruvian-Style Roast Chicken With Tangy Green Sauce

1 cup (packed) cilantro leaves with tender stems

1–2 medium jalapeños, coarsely chopped

1 garlic clove, finely chopped

1 tablespoon extra-virgin olive oil

2½ teaspoons fresh lime juice

¼ teaspoon kosher salt

⅓ cup mayonnaise

1 English hothouse or 2 Persian cucumbers, cubed

1 firm-ripe avocado, cubed

3 scallions, thinly sliced

1 tablespoon plus 1 teaspoon fresh lime juice

1 tablespoon extra-virgin olive oil

¾ teaspoon kosher salt

½ cup cilantro leaves with tender stems, coarsely chopped, plus more for serving