Heat oil in a large saucepan over medium heat; add onion and celery and cook, stirring, until beginning to soften, 2 to 4 minutes. Grate or finely chop 1 clove garlic; add to the pan and cook, stirring, until fragrant, about 1 minute. Add broth, chicken and barley. Bring to a gentle simmer. Cover and cook over low heat until the chicken is cooked through, about 20 minutes. Transfer the chicken to a plate with a slotted spoon. Return the broth to a simmer and cook until the barley is tender, 20 to 30 minutes.

Meanwhile, shred the chicken or cut into bite-size pieces; discard the bone.

When the barley is done, add the chicken, tomatoes and juice, asparagus, peas, salt and a grinding of pepper; return to a simmer. Cover and cook over low heat until the asparagus is tender, about 5 minutes more.

Coarsely chop the remaining garlic clove. Gather basil, orange zest and the garlic and finely chop together. Ladle the soup into bowls and sprinkle each serving with a generous pinch of the basil mixture.

MAKE AHEAD TIP: Prepare through Step 3, cover and refrigerate for up to 2 days. Reheat the soup, thin with broth if desired and finish with Step 4 just before serving.