Heat large deep nonstick skillet over high heat. Add spinach to dry skillet; toss until just wilted, about 3 minutes. Transfer to strainer set over bowl.
Heat 2 tablespoons oil in same skillet over medium-high heat. Add shallots; sauté 5 minutes. Reduce heat to medium; add tomatoes and rosemary and sauté 1 minute. Add broth; cover and cook until tomatoes soften, stirring occasionally, about 4 minutes. Remove from heat. Crush tomatoes with potato masher. Stir in beans and 1 tablespoon oil. Bring to boil over medium-high heat. Reduce heat to medium-low; simmer uncovered until juices thicken, about 15 minutes. (Can be made 2 hours ahead. Let stand at room temperature. Rewarm over low heat.)
Stir spinach into beans. Season with salt and pepper.
