Combine the chiles, adobo sauce, brown sugar, honey, lime juice, mustard, and soy sauce in a small saucepan over medium-high heat. Bring the mixture to a boil, then reduce the heat to medium-low and simmer for 5 to 6 minutes, until the sauce has thickened slightly. Remove from the heat and set aside to cool.
Preheat the broiler. Place the poblano chile on a small rimmed baking sheet. Broil for 10 to 12 minutes, turning the chile occasionally, until charred on all sides. Remove from the oven and transfer to a resealable bag. Let rest for about 20 minutes, until cool enough to handle. Peel the chile, remove the seeds, and dice.
Toss the shrimp with the olive oil and arrange on a large rimmed baking sheet. Season with salt and pepper. Broil the shrimp for 4 to 5 minutes, until cooked through. Transfer to a cutting board and dice.
Preheat the oven to 500°F, or as high as your oven will go. Transfer the pizza dough to a lightly floured work surface and roll out to a thin 15-inch circle. Transfer to a large heavy baking sheet. Sprinkle the Monterey Jack and cotija over the dough. Bake for 8 to 10 minutes, until the crust begins to brown and the cheese is melted. Remove from the oven and top with the pineapple, poblano chiles, corn, and shrimp. Bake for another 3 to 5 minutes, until the ingredients are warmed through. Drizzle the chipotle glaze over the pizza and serve.