Heat oven to 425°F. Toss carrots with oil and salt on sheet; roast 25 to 30 minutes, turning once, until tender with browned edges.
Melt butter in soup pot over medium; soften leeks 5 minutes. Stir garlic and cumin 1 minute.
Add peas, broth, and pepper; simmer partly covered over low 45 to 55 minutes, occasionally stirring bottom, until peas easily collapse.
Add carrots; simmer 5 minutes. Remove from heat; carefully immersion-blend smooth, blade submerged.
Fold in ham; heat over low 5 minutes to 165°F. Add lemon juice and up to measured cup water as needed for thick but pourable soup.
Divide among six bowls, including ham in each.