The Bacon & Egg McMuffin is the iconic McDonald's breakfast item, packing a fried egg, bacon, toasted muffin and cheese in one portable package. McDonald's Executive Chef Dan Coudreaut demonstrates how to cook it yourself at home.
Compared to other McDonald's menu items, the Bacon & Egg McMuffin isn't particularly challenging to replicate (for instance, if you want to make your own Big Mac, the big challenge is replicating the special sauce). You only need a few simple ingredients and some basic equipment to replicate the Bacon & Egg McMuffin (which is referred to stateside simply as the Egg McMuffin). The only unusual item you might not have is an egg ring.
Along with the step-by-step instructions here, Coudreaut offers several useful tips (as he did when sharing the company's own Big Mac instructions). For example, you can easily break the egg yolk just by tapping the centre of the yolk with the egg shell (around 2:18). Another tip is to add a little water to the pan; this creates steam for cooking the egg and getting it nice and fluffy.
For your future reference and if you don't care to watch the video, Yahoo!'s Shine also has the directions and recipe in one page.