I pour the green chile enchilada sauce into a small saucepan and let it simmer over medium heat until it reduces by about a third. This concentrates the flavor so the chicken doesn't turn out watery. It usually takes me 10 to 15 minutes, and I stir occasionally so nothing sticks to the bottom.
While the sauce simmers, I trim my chicken breasts and season them generously with salt and pepper. I place them in the slow cooker and pour the reduced sauce right over the top, along with the can of diced green chiles. I cook everything on high for about 2.5 to 3 hours, or on low for 5 to 6 hours if I'm out for the day.
Once the chicken is fork-tender, I pull it out and shred it using two forks right on a cutting board. Then I return the shredded chicken to the slow cooker and stir it back into that flavorful sauce so every piece soaks it up. This step takes me just a couple of minutes but makes a huge difference in taste.
While the chicken finishes soaking up the sauce, I toss shredded cabbage with the chopped poblano, cilantro, and lime juice in a mixing bowl. I like a little crunch and brightness to offset the richness of the chicken, and this slaw does exactly that. I let it sit for a few minutes so the flavors meld together.
I heat each tortilla in a dry skillet for about 10 to 15 seconds per side. This little step keeps them from tearing and gives them a slightly toasted flavor I really love. I stack them in a clean towel to keep them warm until I'm ready to serve.
Finally, I fill each warm tortilla with a generous scoop of the green chile chicken, then top it with the slaw and a sprinkle of cheese if I'm using it. A squeeze of fresh lime right before eating takes the whole thing over the top for me every single time.