Season beef cubes all over with salt and pepper. Heat a splash of oil in a heavy Dutch oven or cast iron roaster over medium-high heat until sizzling; add half the beef and brown all over in 2 batches. Remove from pan; set aside.

Add onion and gingerroot to pan; sauté until just softened. Stir in broth, scraping up brown bits from bottom of pan. Stir in curry paste and coconut milk. Add reserved beef and any juices.

Cover tightly; cook in a 325°F oven for 1-1/2 hours. Add carrot, sweet pepper and green beans; cook for another 20 to 30 minutes, until veggies are tender. Remove slices of gingerroot and stir in kale. Serve spooned over steamed rice.