Preheat oven to 400°F (200°C) and position a rack in the center. Line a rimmed baking sheet with parchment paper or foil.
Pat the salmon fillets completely dry with paper towels. Place them skin side down on the lined sheet pan, leaving space between each one.
Brush the tops and sides of each fillet lightly with olive oil, then season evenly with kosher salt and freshly ground black pepper. Set aside.
In a small saucepan over medium heat, melt the butter. Stir in the peach preserves, grated ginger, and minced garlic and warm for about 1 minute until glossy.
Remove from heat and whisk in the soy sauce, whole-grain mustard, and lemon juice until smooth. Let cool for 2 to 3 minutes so it thickens slightly.
Spoon or brush a little more than half of the glaze evenly over the salmon fillets. Add the sliced peaches to the remaining glaze in the saucepan and toss gently to coat.
Arrange the coated peach slices around and between the fillets on the sheet pan.
Bake in the preheated oven for 12 to 15 minutes, depending on the thickness of your fillets, until the salmon is mostly opaque and the glaze is bubbling.
Move the oven rack to the top position and switch the oven to broil on high. Broil for 3 to 5 minutes, watching closely, until the glaze caramelizes and the peaches brown at the edges.
Pull the salmon when it reaches 130°F (54°C) at the thickest point. Let it rest on the pan for 5 minutes.
Scatter the chopped cilantro or parsley and toasted sesame seeds over the top. Serve warm with the roasted peaches spooned alongside.