I don't really have a single tea that I could say is my 'breakfast' tea. I tend to drink something different each day depending on what I'm having for breakfast. The other morning my husband decided that we needed French toast with maple syrup and bacon - not perhaps the wisest decision on a weekday morning when (as it turned out) he had a relatively early meeting to get to work for, but that's as may be - which set me hunting through my pantry for an appropriate tea to go with such a hearty, savoury yet also sweet, breakfast.
It's common for Western-style breakfasts to be accompanied by powerful, wakey-uppy type teas, typically blends involving Assam and other brisk black teas that take milk and sugar well. See for example this brief Wikipedia article on English Breakfast tea, and for my thoughts on some common breakfast blends, have a peek here and here. If I'm going for one of these kinds of teas, Irish Breakfast would be my pick. However, I actually opted for some genmaicha to have alongside our impromptu fancy breakfast.
Genmaicha is a Japanese tea blend containing green tea and roasted rice kernels; perhaps a slightly perverse choice for morning drinking as the lower proportion of tea leaves means that it is significantly lower in caffeine content. It's not something that I drink on a very regular basis; it's an intensely savoury tea that tastes predominantly of the roasted rice with little green tea flavour (at least this is the case with the brand that I have, which is made by Ujinotsuyu). It is an excellent partner with many kinds of savoury food though, and went quite well with the smoky, sweet flavours of the maple syrup and bacon.
Other teas that you might like to consider with a substantial savoury breakfast include Lapsang Souchong (or add a little pinch to your regular plain black tea) or a darker-roasted wulong (oolong) like Da Hong Pao. Chinese gunpowder green could be good too, and plain or vanilla-flavoured rooibos would also be a great herbal option. I'd definitely steer clear of anything very flowery or too light.