In a spacious pot, warm 1/4 cup plus 2 tablespoons of the olive oil over medium-high heat. Add the sliced garlic, stirring frequently, and cook until it turns a delicate golden color, about one minute. Begin incorporating the chard leaves a handful at a time, letting each batch wilt slightly before adding the next. Season generously with kosher salt and freshly ground black pepper. Cook, stirring occasionally, until the leaves are tender and the liquid has mostly evaporated, roughly 8 minutes. Transfer the cooked leaves to a bowl and set aside. Wipe the pot clean with a paper towel.

Return the pot to the heat and pour in the remaining 2 tablespoons of olive oil. Add the chard ribs and cook over medium-high heat, stirring occasionally, until they become crisp-tender, about 5 minutes. Reintroduce the wilted chard leaves to the pot, mixing well, and adjust the seasoning with additional salt and pepper to taste. Transfer the chard mixture to a serving bowl, sprinkle with the freshly grated lemon zest, and serve immediately while warm.