The "slow fry" fried egg
Or, for those culinary historians among us, the "Point Method" courtesy of French chef Fernand Point.
For those that enjoy their sunny side up eggs with a warm runny yolk and creamy whites without any hint of charred or crisp edges, then this is the perfect method me thinks.
Not complicated, and this is what I do.
1. Coat a pan with your fat of choice. I like bacon grease or duck fat.
2. Turn the heat on the stove to the lowest setting and heat the pan just long enough for the fat to coat the pan.
3. Crack an egg into a separate bowl.
4. Then slide the egg into the pan.
5. Cover the pan with a lid.
6. Let it sit there, covered, on the lowest heat setting for 2 minutes.
7. Then turn off the heat, and let it sit for another 2 minutes or until the whites turn from translucent to a milky white.
9. Heat up the remaining fat in the pan, then gently drizzle *around* the whites of the egg (not on top)
10. Garnish with a healthy sprinkle of sea salt.
11. Dig in.
Growing up, we had what my mother called 'Guardian Ware Eggs'.
She'd use the small Guardian Ware pan, fixed them just like you described, but she'd sprinkle in a little water before she put the glass lid on.
We never had crispy edges with those eggs. I'm not a crispy edge fan. Hers were perfect.
Eric Ripert has a similar approach to omelets, very much contra the classic high heat/sizzling butter method. He melts the butter over low heat, puts the blended egg into the pan when the butter is just hot, and keeps egg and cheese or whatever at a just-melting temperature. Works very well; gives a tender non-rubbery omelet.
I like my fried eggs exactly as described in the OP - the slightest hint of crispy and I'm likely to throw them away and start again. Never seem to have much trouble cooking them as I like them - low heat, a little basting of the yolk to keep it in pace with the whites - ready just as the yolk is turning opaque.