Preheat your grill on medium-high, about 350°F, leaving one side of the grill cool. (If you have a 3-burner gas grill, leave 1 far side off; if you have a 2-burner grill, leave 1 side off. Clean the grill grates.
Place a 10-inch cast-iron skillet directly on the grates on the hot side of the grill. Close the lid and let the skillet preheat for 10 minutes.
In a medium bowl, whisk the eggs, cream, and a large pinch of salt and pepper together.
Add the ghee to the skillet; using a flame-resistant mitt, grasp the handle and swirl the pan to coat. Pour in the eggs. Use a silicone spatula to push the eggs at the edges inward, gently folding them over. Continue cooking and folding until the eggs are almost set but still slightly wet on top, 7 to 8 minutes. Move the skillet to the cool side of the grill.
Turn the hot side of the grill up to high and oil the grates. Place the avocado halves cut side down on the hot side and grill until you see grill marks and the flesh turns bright green and easily pulls away from the grates, 3 to 4 minutes. Next add the tortillas and grill until warmed through and lightly charred, about 1 minute per side.
Remove the egg skillet from the grill. Peel the skin from the avocado and thinly slice. Place 2 tortillas on each of 4 plates and top each with a few slices of avocado followed by the scrambled eggs, a sprinkle of cheese, sliced radish, a scoop of salsa, and some cilantro sprigs. Serve immediately with lime wedges on the side.