Preheat the oven to 450 degrees F. Toss the bread cubes with 2 tablespoons schmaltz, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Spread out on a baking sheet and bake until deep golden and crispy, 10 to 12 minutes. Transfer to a large bowl and set aside. Place the pancetta on the same baking sheet and bake until crispy, 2 to 3 minutes. Transfer to a paper-towel lined plate and let cool, about 5 minutes. Crumble the pancetta and set aside.
Meanwhile, sprinkle the chicken breasts with 1/2 teaspoon salt and a few grinds of pepper. Set a 6-quart Instant Pot® to saute on high (see Cook's Note) and wait for it to say "hot" (this should take about 4 minutes). Add the butter and the remaining 2 tablespoons schmaltz and stir until the butter melts, about 1 minute. Add the chard stems and the leeks and cook, stirring occasionally, until the vegetables have softened, 4 to 5 minutes. Stir in the wine, thyme, 1/2 teaspoon salt and a few grinds of pepper. Turn the machine off and add the chicken breasts.
Follow the manufacturer's guide for locking the lid and preparing to cook. Set the pot to pressure cook on high for 6 minutes. After the pressure cook cycle is complete, follow the manufacturer's guide for quick release and wait until the quick release cycle is complete. Be careful of any remaining steam and unlock and remove the lid. Transfer the chicken to a medium bowl and shred. Add the chard leaves to the pot and stir constantly until wilted, 1 to 2 minutes. Fold in the bread cubes and the shredded chicken and stir until well combined. Serve in bowls with the pancetta on top and lemon wedges on the side.
Settings may vary on your Instant Pot® depending on the model. Please refer to manufacturer's guide.
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