To make the slaw: In a large bowl, combine the cabbage, cilantro, green onions, lime juice, and vegetable oil. Toss the season with salt. Set aside.
In a heavy pan or skillet, heat the vegetable oil over medium heat. Season chicken breasts with salt, if desired, then add breasts and cook for 3 to 4 minutes per side (depending on thickness), until they are just cooked through in the center. Transfer to a plate and set aside.
To make the cilantro pesto: In a food processor combine the cilantro, garlic, jalapeño, pepitas, vegetable oil, and lime juice. Pulse until well combined and season with salt.
Using two forks, shred the chicken. Combine the chicken with the cilantro pesto in a mixing bowl and toss to coat. Add salt if needed.
Rub the tortillas with the vegetable oil and set them directly over a gas burner until they are slightly charred and hot, about 10 seconds, turning them with tongs. You can also heat them directly in the bottom of a very hot dry skillet or heavy pan, using tongs to turn them. Stuff each tortillas with some of the chicken mixture and a scoop of the slaw, and garnish with a few slices of avocado and jalapeño. Serve immediately.