In a small dry skillet over medium heat, toast the sliced almonds for 2–4 minutes, stirring often, until fragrant and lightly golden. Transfer to a plate to cool so they stay crisp.

Whisk together the olive oil, balsamic vinegar, lemon juice, honey, Dijon mustard, and a pinch of salt until emulsified. Taste and adjust sweetness or acidity as needed.

Slice peaches thinly. For grilled peaches: brush slices lightly with olive oil and grill 1–2 minutes per side until caramelized. Allow to cool slightly.

Place arugula in a large bowl. Add sliced peaches, red onion, and most of the toasted almonds. Drizzle three-quarters of the dressing and toss gently to coat. Top with goat cheese, basil, remaining almonds, and season with salt and pepper. Finish with a light drizzle of balsamic glaze if desired.

Serve immediately. Add grilled chicken or shrimp to make it a main course, and enjoy with crusty bread or a chilled beverage.