I think you might be referring to the shoes I took to Morocco, which would be TOMs Botas. They have several different designs now, but I linked to the specific pair that I own. They were surprisingly warm and comfy, and I even went hiking in Morocco with them and they held up incredibly well. They’re a definite upgrade from the usual TOMs shoes, with a sturdier sole. They also slip on and lace-up so it can make airport security easier (just slip-on) or ensure your shoes don’t come off (lace them up too).
On every trip, I always have a debate about what shoes to bring. Standard practice for me seems to be a pair of Converse (since that’s what I wear most of the time anyway) and a pair of hiking boots (Merrel, since I had two pairs, they last forever, and they’re very comfy). I did really love the Botas in Morocco, though, and if I needed to dress up while on the trip, I’d probably need a nice pair of boots (more practical than heels while traveling - such as a pair of Frye’s or Dr. Martin’s boots) or maybe some nice flats, since they pack much smaller. If I’m not going to be in areas where hiking is lightly, I leave the Merrel’s at home, and likewise adjust my shoes according to weather (screw the dress boots if I’m going somewhere hot and tropical!).
I’m unfortunately not in SE Asia right now as I had hoped, but rather in San Francisco and Los Angeles, and even with only carry-on, I managed to pack two pairs of boots, a pair of heels, and my sneakers, which is crazy to me, because I usually only travel with one, maybe two pairs of shoes. And depending on the trip, really, you shouldn’t need more than two pairs. Two pairs are a really, really good idea though, because if you get soaked in your travels, you’ll want that other pair of shoes - even if they’re just a pair of flip flops.