Heat the oil and garlic in a large skillet over medium-high heat. Once the garlic starts sizzling, reduce the heat to medium and cook until it turns golden, about 2 minutes. Transfer the garlic and all but 1 Tbs. of the oil to a food processor. Raise the heat to medium high, add the spinach, and sauté, stirring, until it wilts, about 2 minutes. Season with salt and pepper and set aside.
Put the cannellini beans, thyme, and 2 Tbs. water in the food processor with the garlic. Process until fairly smooth, adding another 1 or 2 Tbs. water if needed. Season with salt and pepper. If making ahead, refrigerate the white bean purée; bring it to room temperature before assembling.
To assemble, top the crostini with the bean purée, a portion of spinach, and slices of the sun-dried tomato and serve