Take a 9x13 pan or casserole dish and oil the inside with a little olive oil. Set aside and preheat your oven to 450° F.
In a big saute pan, heat some olive oil until shimmering, and add the onions and thyme. Toss around a little bit until the onions are coated and turning translucent, about 2 minutes. Add the breadcrumbs and toast them with the onions for a few more minutes, until they start to turn golden. Season with salt and pepper. Remove from heat and let cool as you prep the next step.
In a medium bowl, blend the ricotta with the milk/cream to loosen it up. Add the breadcrumb/onion mixture. Put half this mixture in the bottom of the pan. Put the ham down in a single layer over the breadcrumb/cheese mixture, and then top the layer of ham with the rest of the breadcrumb/cheese mixture. Make six indents on top of the bed of ricotta, big enough that the yolks can settle into them comfortably.
Crack your eggs into the indents and bake until the whites are done and the yolks are set to your likeness. If using a metal sheet pan, start checking at 10 minutes, gently nudging the yolks and whites to see if they're the consistency you like. This can be anywhere from 10-30 minutes, so be vigilant and keep checking, but it'll likely be done before 20 minutes. For a ceramic casserole dish, do the same, but know that it might take 30 minutes in this case (still, keep checking). When you feel it's ready, serve!