Preheat oven to 425°F Spray large rimmed baking pan with non-stick spray.
Heat oil in large nonstick skillet over medium-high heat. Add shallots and cook, stirring frequently, until softened about 3 minutes. Add half of spinach and 3 tbsp of water. Cook, stirring occasionally, just until spinach wilts, about 4 minutes. Add remaining spinach and cook, stirring frequently just until wilted and liquid evaporates, about 2 minutes. Remove skillet from heat. Stir in bread crumbs, ham, and pine nuts.
Place mushroom caps in baking pan, gill sides up. Fill caps evenly with spinach mixture, mounding it slightly. Add remaining 1/4 cup water to baking pan. Bake until mushrooms are tender and filling is hot, about 25 minutes.