Yes, I post a lot of brunch recipes. It's easy to be creative at brunch, when you can ignore pesky things like nutritional value and the need for a balanced meal. Besides, it's really my favorite meal: eggs were the first thing I learned to cook. Anyway, this is for you Levantine food fans reading.
za'atar potato cakes
1 cup cold leftover mashed potatoes
1/2 cup grated parmesan or similar 
1/2 small onion, grated
1/2 tsp Aleppo pepper or harissa 
1/2 cup za'atar 
2 to 3 Tbs olive oil
quantities per person; makes two cakes. also, see notes below
Mash together the potatoes, cheese, onion, and pepper/harissa until completely blended. With damp hands, form two flat, round patties about 1/2" thick. Using a bowl just larger than each patty, coat them with za'atar, turning them over carefully a few times until completely coated.
Heat the olive oil in a nonstick pan or griddle to medium-high heat (325F). Carefully slide the cakes into the pan, and then let fry for 3-5 minutes without touching them. Once they've formed a nice brown crust on the bottom, flip them with two spatulas, and fry for another 3-4 minutes on the other side.
Once they have a crust on both sides, slide them onto plates and let cool for 10 minutes to firm them up. Serve with poached eggs or crispy fried eggs on top. Give your guests sharp knives, since the cakes are delicate and will tend to mash instead of cut.
1. Any dry but still melty cheese, such as parmigiano, pecorino romano, dry jack, or aged gouda. Dry non-melting cheeses like myzithra, will make for cakes which are too delicate. Semisoft cheese will result in cakes that melt and are gushy, like in the photo below (still tasty, but hard to eat). Conceivably, one could make vegan potato cakes using vegan "cheese" but I haven't tried this.
2. You can adjust the pepper content according to your palate. At the low end of the scale, use 1/2 tsp smoked paprika. If you're me, you use, 1/2 tsp Aleppo pepper and 1 tsp harissa.
3. You'll need to get real za'atar, or this recipe will suck. Sadly, a lot of spice companies, including Penzey's, are currently selling something they call "zatar" which contains none of the actual herb za'atar (a close relative of oregano) at all; do not use these. If the za'atar you have isn't dark green in color, it's the bad kind. If you have no Arab market in your area, then here's a recipe for fake za'atar which doesn't suck:
1/4 cup dried oregano (pref. Turkish or Greek)
2 Tbs dried thyme
1 Tbs marjoram
1 Tbs sumac
1 Tbs sesame seeds
Put the oregano, thyme, marjoram, and sumac in a spice grinder. Pulse several times until reduced to a coarse powder. Add the sesame seeds. Store sealed, or in the fridge.