Whisk the eggs together with the cream. Season with salt and pepper.
Melt the butter into a skillet over medium-low heat. If the butter bubbles, sizzles, or browns quickly, adjust heat down to low. You want the skillet to be moderately warm but not too hot.
Pour the eggs into the skillet and let them cook in the warm butter for 2 minutes without moving. The bottom should begin to set up (not brown; keep an eye on the heat!) but the top should still be mostly liquid.
Once the bottom begins to set up, sprinkle the spinach, cheddar, and dill on top. Let stand 1 minute and then use a rubber spatula to begin breaking up the eggs. Don’t overwork them! Continue stirring gently, every minute or two or so until the eggs reach your desired consistency. I like mine a few minutes past custardy, soft eggs with large curds that have set up but aren’t firm. Cook until you’re happy with the consistency!
Taste and season with salt and pepper.