Step 1In a skillet over medium heat, cook the onion with ½ teaspoon salt and 1/8 teaspoon pepper, or to taste, in 3 tablespoons of the olive oil until softened and pale golden, 5 to 7 minutes. Stir in the garlic, cook a moment longer, then stir in the huacatay and a little more salt and pepper. Cook until the greens wilt, 2 to 3 minutes. Lower the heat, add ¼ cup water, cover the pot and cook until the greens are tender, about 10 minutes, adding another ¼ cup water, or as needed, if mixture seems dry.
Step 2Using an immersion blender and beaker or a small food processor, combine the huacatay mixture with ¼ cup water and purée. Slowly add the remaining olive oil as you continue blending. The salsa should be thick, but pourable, with a bit of texture. Scrape the salsa into a bowl, thinning with a little more water or olive oil as needed and adding additional salt and pepper to taste as needed. Serve at room temperature. The leftovers may be covered and refrigerated up to 5 to 6 days.