For the pita chips: Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. In a small bowl, combine the chili powder and cumin. Drizzle the tops of the pita breads with the oil and sprinkle with the spice mixture and salt. Cut each pita bread into 8 wedges and arrange in a single layer on a baking sheet. Bake until crisp and golden, about 10 minutes.
For the dip: Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Butter a 9-inch round ceramic deep-dish pie pan or a 1-quart baking dish.
Place a large skillet over medium-high heat. Add the oil and bacon and cook until crispy, about 8 minutes. Remove the bacon and drain on paper towels. When cool enough to handle, crumble into 1/2-inch pieces. Set aside. In the same skillet, add the oil (if needed), shallots, garlic, artichokes, 1/2 teaspoon of the salt and pepper. Cook over medium-high heat until the shallots are translucent and the artichokes begin to brown, about 8 minutes.
Transfer the vegetables to a food processor. Add the mascarpone cheese, sour cream, mayonnaise, lemon juice, 1/2 of the cooked bacon pieces and the remaining 1 teaspoon salt. Pulse until combined but still chunky. Place the dip in the prepared baking dish and sprinkle with the remaining bacon pieces. Bake until just warmed through (do not let the dip boil), 10 minutes. Serve the pita chips alongside.