1Trim the chops, season to taste and dredge in flour. Heat oil and butter in a large frying pan and add chops. Cook for 2-3 minutes on medium high heat or until chops are well browned.
2Pour in wine, broth and mushrooms. Reduce heat and slow braise, covered for 20-30 minutes, or until lamb is tender. You may need 2 pans for this, or sear in batches then stack in a larger pan for braising, rotating chops during cooking.
3Remove meat from pan, cover with foil. Continue to simmer sauce on a higher heat until thickened to desired consistency. Return lamb to pan with the sauce and heat through, spooning sauce over chops.
4While lamb is braising, cook the squash. Heat olive oil in a separate, non-stick pan and add shallot. Cook for 1 minute, add squash, and stir for additional 3-4 minutes, or until golden brown.
5Add broth and turn heat to low. Cover and simmer for 10-12 minutes, or until tender.