Heat olive oil in a large skillet over medium-low heat. Add shallots and cook, stirring occasionally, until the shallots have become totally softened, around 20 minutes. Add Swiss chard and garlic, and sauté for 5 more minutes.
Add tomato paste and black pepper. Cook, stirring frequently, until the tomato paste has started to cook in the oil a bit, deepening in color, about 2 minutes. Remove from heat and transfer about half the mixture to a resealable container.
When cooking the shallots, be sure to cook them low and slow. You don’t want to fry the shallots necessarily, but rather braise them in a sense. So keep your heat low and be patient; you will end up with sweet and tender shallots that will melt in your mouth.