Cut the stems and center ribs from the chard. Slice the stems into 1/2-inch pieces and coarsely chop the leaves separately.
In a large dutch oven, heat the EVOO and butter over medium-high heat. Add the onions, garlic, 1 tsp. salt and 3/4 tsp. pepper; cover and cook, stirring occasionally, until the onions begin to soften, 7 to 8 minutes. Mix in the chard stems, cover and cook, stirring occasionally, until just tender, about 8 minutes (lower the heat slightly if the mixture looks dry). Add the chard leaves in batches, stirring until wilted. Cover and cook, stirring once, until tender, about 5 minutes; season with salt and pepper. Drain in a colander set over a bowl, then transfer to a platter and sprinkle with the pine nuts.