1. Peel the potatoes, slice them into bite-sized wedges and put them in a bowl of cold water.
2. Trim excess fat from the lamb and cut it into approximately 1 1/2 inch pieces.
3. Pat the meat dry with paper towels and lay it on a wax paper-lined baking sheet in a single layer. Sprinkle with 1 teaspoon of salt and a few grinds of pepper and turn the pieces, to coat them. Sprinkle on the flour and toss to coat. Remove any excess flour.
4. Heat 2 tablespoons oil over medium heat in a heavy lidded pot. Brown lamb on all sides in two or three batches (don't overcrowd the pot), 3-4 minutes per batch, adding more oil if necessary. Transfer lamb to a plate as it is browned, and set aside.
5. Add onions to the pot and sauté, stirring, for about 3 minutes, until lightly browned. Add garlic and cook, stirring, for 30 seconds. 
6. Pour in wine and cook for 30 seconds, stirring. Add tomato paste and stir until blended with the wine. 
7. Return lamb to the pot along with any accumulated juices. Add the rosemary and 3 cups of the chicken broth (meat should just barely be covered with liquid). Bring the contents to a simmer, cover and cook for 1 hour. 
8. While the stew is simmering, bring a saucepan of salted water to a boil. Drop the green beans in and boil for about 3 minutes, until just crisp-tender. Drain the beans and quickly transfer them to a bowl of ice water to cool them quickly and ensure they stay crisp and bright green. 
9. Season broth with salt and pepper, to taste. Submerge the carrots and potatoes in the stew, adding the remaining 1 cup of broth, if necessary. Bring to a simmer. Cover and cook for 25-30 minutes, until vegetables are tender.
10. Drain the green beans and submerge them in the stew along with the peas. Cover and simmer 5 minutes more, to warm the beans and peas. Serve hot.