Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Cut out 3-inch stars from the wonton wrappers using a cookie cutter; lightly brush both sides with vegetable oil and arrange on the prepared baking sheets. Sprinkle with salt. Bake, switching the pans halfway through, until the chips are golden brown and crisp, 12 to 15 minutes; let cool on the baking sheets.
Preheat the broiler. Put the poblanos on a separate baking sheet and broil, turning once, until charred, 10 to 12 minutes. Transfer to a bowl, cover with plastic wrap and let sit 10 minutes. Peel off the skin and remove the stems and seeds. Roughly chop the poblanos.
Combine the poblanos, canned chiles, cream cheese, 1/2 cup shredded cheese and 1/4 cup enchilada sauce in a large bowl. Beat with a mixer on medium-high speed until smooth, 2 to 3 minutes. Transfer to a shallow 1 1/2-quart baking dish and top with the remaining 2 tablespoons enchilada sauce and 3/4 cup shredded cheese. Bake until the dip is bubbling, about 20 minutes. Top with pickled jalapenos and serve with the star chips.