Toast the bread to your liking.
Spread it with half the butter while warm.
Halve, pit, and slice the avocado. Arrange slices onto buttered toast. (Or you can mash it if you prefer.)
Sprinkle with the lemon juice, and some flaky salt and freshly ground black pepper.
Crack the eggs into a bowl and pour in the cream. Add the fine sea salt and about ⅛ teaspoon freshly ground black pepper.
With a fork, beat the eggs until the contents of the bowl are an even, creamy yellow, with no visible bits of yolk or white.
Set a heavy 8- or 10-inch nonstick pan over medium-low heat. Add the butter. When it's melted and foamy, pour in the eggs.
Let the eggs sit undisturbed just until you can see around the edges that they've set on the underside. Then, in a few gentle motions, use a silicone spatula to pull the edges of the eggs into the center.
Repeat this process — letting the underside set, and then pulling the edges to the center — once or twice more as needed. You can lift the pan up off the heat a bit to control the temperature so the eggs set without browning.
Just before you think the eggs are perfectly cooked, remove the pan from the heat. They'll keep cooking a bit with their residual heat and end up just right.
Arrange eggs over avocado toast, sprinkle with additional flaky salt and pepper if you like, and serve right away.