Dry the steak well and season with salt and pepper.
Heat a cast iron skillet over high heat until just beginning to smoke. Add avocado oil to the pan and then add the steak, cook until well browned on both sides, turning often, about 8-10 minutes total. Remove steak from pan and set aside to rest.
In the same pan, add the cherry tomatoes and pepper flakes. Cook over high heat, stirring often until the tomatoes begin to break down. Add minced garlic and cook until fragrant, another minute. Add coconut aminos and butter and cook together another two minutes, adding water if needed to thin the sauce. Off heat, add lime juice.
Slice steak against the grain. Plate and top with the cherry tomato sauce. Garnish with fresh herbs, if desired and serve with extra lime slices.