Cut off ends of each "whole" squash. Scrape dark bruises off skin. Do not peel.
Wash "whole" squash in warm salty water. Rinse in clear water. Pat dry.
Slice each "whole" squash into thin rounds.
Spread slices in a single layer on paper towels. Salt and allow to "sweat" for 10 minutes. Blot dry with fresh paper towels.
Flip slices over and repeat with salt. After 10 minutes, blot dry with fresh paper towels. The salt seasons and releases water from the squash for better sautéing.
Remove skin from one yellow onion. Slice into 1/4 inch-thick rings. Slice rings in half. Set aside.
In a large 10" saucepan, combine ONE tablespoon of olive oil and ONE tablespoon of unsalted butter. Melt over low-medium heat.
Spread squash and onions in one layer. Set aside remainder. Sauté over medium-high heat until desired tenderness for 1 to 2 minutes. Flip over and continue cooking until desired tenderness. Do not leave stove. Squash and onions cook quickly.
Remove from skillet and drain on paper towels.
Carefully wipe hot skillet clean with thick towel or thick paper towels.
Repeat above instructions to cook the remaining squash and onions.
Serve hot or warm.