Peel and slice 2–3 medium yellow, Spanish, or sweet onions into even strips — uniform thickness prevents uneven cooking. Use a 12-inch skillet max for 2 large onions; overcrowding causes steaming and extends cook time. Use 1 tbsp butter + 1 tbsp olive oil (butter alone can burn over the long cook). Add ½ tsp salt early to draw out moisture and speed up softening.

Heat a 12-inch skillet over medium-high. Add butter and olive oil; once butter melts, add sliced onions and toss to coat. Season with ½ tsp salt immediately. Cook on medium-high for 5–10 minutes, stirring occasionally, until onions soften and turn lightly golden. Reduce heat to medium or medium-low — this is critical. Do not rush with high heat or the onions will burn, not caramelize. Continue cooking 35–45 minutes (total 35–55 minutes), stirring every few minutes. If the pan looks dry or bits are sticking, deglaze with a splash of water, broth, wine, or vinegar and stir to lift the fond. Time-saving option: Add ½ cup water with the onions at the start and cover with a lid. Steam wilts them in minutes. Once water cooks off and onions are soft, remove lid and continue uncovered until deeply browned.

Done when deep golden-brown, very soft, and jammy — not pale or blonde. Volume will have reduced significantly. Pale onions at 20 minutes are just softened, not caramelized; keep going. Taste to confirm: zero sharpness, fully sweet and savory. No resting needed. Refrigerate leftovers in an airtight container. Use on burgers, flatbreads, pasta, dips, or grilled meats.