Mix cracker flour and salt; cut in butter to pea-size pieces. Stir in 2 tablespoons ice water, adding reserved water only as needed to hold dough. Flatten into disk; wrap and refrigerate 20 minutes.
Melt soup butter in 6-quart pot; cook onion 5 minutes. Add potatoes, broth, thyme, soup salt, and pepper; simmer 15 minutes until potatoes very tender.
Meanwhile, heat oven to 400°F. Roll chilled dough between parchment to 1/8 inch thick; cut 12 small triangles on lined sheet. Bake 15 to 18 minutes until golden and crisp.
Immersion-blend potato base smooth, blade submerged. Add carrots and pearl onions; gently simmer 10 to 12 minutes until tender, stirring bottom often.
Add peas, turkey, and milk; gently heat 5 to 8 minutes until turkey 165°F. Avoid hard boiling.
Divide among 6 bowls; serve 2 crackers each against rim or alongside just before eating.