Heat 1 tablespoon olive oil to a large pot over medium heat. Add chopped onion and season with salt and pepper. Saute stirring occasionally, until softened, about 5 minutes. Add thinly sliced garlic to pot. Cook, stirring constantly, for 1 minute. Add broth, potatoes, cabbage and 2 cups water; bring to boil Reduce heat to medium. Simmer soup until potatoes are tender when pierced with a knife, about 10 minutes.
Roast raw pine nuts on a flat tray in a 350-degree oven for about 10 minutes, shaking halfway through. They may also be toasted on top of the stove in a heavy skillet, stirring often until they turn golden.
Add Swiss chard and toasted pine nuts to pot and cook for 5 minutes. Stir in 3 cups spinach and 2 teaspoons lemon juice until spinach is wilted. Puree soup with a food processor until smooth. Add 1/2 cup cream.
Meanwhile, to make spinach gremolata, chop the remaining 1 cup spinach; place in small bowl. Add lemon zest, finely grated garlic clove, and the remaining 1 tablespoon of olive oil to chopped spinach; toss to coat. Season spinach gremolata to taste with salt, pepper and more lemon juice, if desired.
Season soup, as needed, with salt and pepper. Divide among bowls. Mound spinach gremolata on top of soup in serving bowls. Serve immediately.