Heat 1 tablespoon oil in a deep 12-inch skillet over medium heat. Cook spinach for 2 to 3 minutes until wilted and its moisture evaporates, then transfer to a bowl and cool for 10 minutes; cooling is included in prep time.
Mix cooled spinach with ricotta, sun-dried tomatoes and Parmesan. Season chicken with 1/2 teaspoon salt and pepper, divide filling among the flattened breasts and roll each from a short end, securing each seam with 2 wooden toothpicks.
Add remaining oil to the same skillet over medium heat. Brown rolls for about 2 minutes on each of 4 sides, then transfer to a plate while partly cooked.
Cook shallot in the skillet for 2 minutes, then stir in garlic for 30 seconds. Add wine and simmer for 2 minutes, scraping the bottom, then add broth and remaining salt.
Return chicken rolls and their juices, cover and simmer gently for 15 to 20 minutes, turning once, until the center of each filled roll reaches 165°F. Transfer to a clean board and rest for 5 minutes.
Stir beans into the sauce, mashing about one-quarter of them with a spoon, and simmer for 4 minutes until hot. Stir in lemon juice, remove all 8 toothpicks from the chicken and cut each roll into 2 thick pieces. Serve with the white beans and pan sauce.