Heat the oven to broil and arrange a rack in the middle. Line a baking sheet with aluminum foil and set aside.
Lay a jalapeño on your work surface so that it sits flat without rolling. Make two cuts forming a “T” by first slicing down the middle of the chile lengthwise from stem to tip, then making a second cut perpendicular to the first about 1/4 inch from the stem, slicing only halfway through the chile (be careful not to cut off the stem end completely). Carefully open the flaps to expose the interior of the chile, and, using a butter knife or small measuring spoon, scrape the inside to remove the seeds and ribs. Repeat with the remaining peppers; set aside.
Place the cream cheese, chicken, salsa verde, cilantro, and salt in a medium bowl, season with freshly ground black pepper, and mix until smooth and evenly combined. Transfer the mixture to a quart-size resealable plastic bag, cut one bottom corner off to make a 3/4-inch-wide opening, and squeeze the mixture into the chiles until just filled (be careful not to overfill). Insert a toothpick widthwise through each chile to secure the flaps and filling. Place the filled chiles on the prepared baking sheet in two evenly spaced rows of six.
Broil for 4 minutes, rotate the pan, and continue to broil until the peppers are starting to char and the filling is browned and bubbly, about 4 minutes more. Remove from the oven, and remove the toothpicks if desired. Let cool for 5 minutes before serving.