Satay is most commonly served with peanuts, but I went Italian and reimagined it with Parmesan pesto. The cheese, to me, almost acts as nuts would, offering richness and deep flavor that the chicken really needs.
Swap option: You can use a couple of chicken breasts in place of the tenders here.
Preheat the oven to 350°F.2.
Season the chicken with salt and cut into 1½- to 2-inch pieces. Arrange them on skewers, 2-3 pieces per skewer.3.
In the bowl of the food processor, "pulse" the garlic, basil leaves, sugar, salt and pepper until coarsely chopped. Through the top of the food processor, stream the olive in gradually (with the food processor running). Transfer the mixture to a bowl and stir in the Parmesan cheese. Taste for seasoning and adjust as needed.4.
Heat a large skillet over high heat and add the oil. When the oil begins to smoke lightly, remove the pan from the heat and add the skewers in a single layer. Cook them on one side until nice and browned, 3-5 minutes, then turn on the second side and cook for an additional 5-6 minutes, until cooked through.5.
Arrange the skewers in a single layer on a baking sheet lined with parchment paper. Place in the oven for a few minutes to finish cooking. The chicken should register 165°F on an instant-read thermometer.6.
Spoon the pesto generously over each of the chicken skewers, sprinkle with salt and top with squeezes of the lime juice. Transfer the skewers to a serving platter.