I'm not a low carb kind of person but when the ingredients present themselves to me, said ingredients are delicious, and it's an easier way to bind the original recipe I'll take it. Carrots have lower water content than potatoes. When making traditional latkes you'll find yourself squeezing out the water from taters but in this case you have about half the work to do. Labne is also a nice twist on sour cream, richer and balances out the *health* of the carrots.
What you need to do:
Peel your potatoes and in a food processor use the julienne blade. Shred and set aside to drain (I use cheesecloth and WRING it out).
Peel your carrots and repeat what you did with potatoes. Mix potatoes and carrots together adding in everything but your eggs. Whisk eggs and then fully combine into your mixture.
Heat on medium heat a large non-stick pan and spray with an oil. Because I'm me I'll do a big glog of olive oil per batch. Once the pan is hot place heaping tablespoons and plop into pan. I'll do about four blobs (2 inches wide and an inch thick) for 14 inch pan because I don't want them to crowd. I'll also pat down the blob so they're all even and flat making them easier to flip. Basically the rule here is turn that blob into a patty.
Once the bottom is browned (about five minutes) flip your patties (they've evolved from their blob state) and cook the other side around five minutes.
Set aside to cool and top with labne at abandon. I tend to do a big dollop and then garnish with either dill or pepper but you could get wild and start adding salmon or whatever else you have in your fridge.