Trim the ends from the Swiss chard stems.
Cut off and discard any wilted or yellow parts of the leaves.
Strip the stems from the leaves and cut the stems into 1/2-inch thick slices.
Cut the leaves lengthwise in half, then crosswise into ½-inch-wide strips.
Wash the leaves and stems thoroughly, then drain well.
Bring the salted water to a boil in a large pot.
Add the potatoes and cook for 10 minutes.
Add the Swiss chard and cook until the potatoes and chard stems are very tender, another 20 to 30 minutes.
Drain in a colander.
In a large skillet, heat 2 tablespoons of the olive oil over medium heat.
Add the garlic and cook just until it begins to brown, about 1 minute.
Add the drained Swiss chard and potatoes and season them lightly with salt and pepper.
Cook, stirring and mashing the potatoes, until the liquid has evaporated and the potatoes are coarsely mashed; if the potatoes begin to brown, reduce the heat to medium-low.
Add the remaining 2 tablespoons of olive oil, season to taste with salt and pepper, stir, and serve hot.