Place steak in a shallow glass dish and pour chimichurri over the top. Turn to coat and allow to marinate for at least 10 minutes, to overnight.
Add all of the Creamy Avocado Salad Dressing ingredients to a blender and blend until smooth, scraping the sides down as needed. Taste and add additional lime juice or water if you'd like it thinner. Season with salt and pepper, to taste. Set aside or refrigerate until ready to use.
Heat a grill, grill pan, or skillet over medium-high heat. Use non-stick spray or olive oil if the pans are not non-stick. Once hot, add the steak and cook for 3-5 minutes on each side, or to your desired doneness. Remove to a cutting board and allow to rest for 5-10 minutes before slicing against the grain in 1/2" thick slices.
Arrange remaining salad ingredients, greens first, in a large bowl (or divided amount smaller bowls) and top with steak slices. Drizzle (or douse, if you prefer) with the creamy avocado dressing, and top with tortillas strips. Bon appetite!