Heat 1/2 cup of the olive oil in a large skillet over medium-high heat. Add 2 cups of the Brussels sprouts and cook, stirring occasionally, until golden and crispy, 5 to 7 minutes. Season with salt and pepper, then place on a paper towel-lined plate with a slotted spoon to remove any excess oil. Wipe out the skillet.
Heat the remaining 1/4 olive oil over medium-low heat in the skillet. Add the pistachios and rosemary and cook, stirring occasionally, until the pistachios are toasted and golden, 3 to 4 minutes. Remove and discard the rosemary sprigs. Transfer the pistachios with a slotted spoon to a cutting board to cool, season with salt and pepper, then chop finely. Pour the oil from the skillet into a medium heatproof bowl and let cool.
Add the lemon juice and zest to the medium bowl and whisk to combine. Season the dressing with salt and pepper and set aside.
Combine the cooked Brussels sprouts with the raw Brussels sprouts in a large bowl. Add the pistachios, cranberries and cheese; season with salt and pepper. Add the dressing and toss to combine. Top with sumac and enjoy.
For a heartier meal, add shredded turkey or rotisserie chicken.