Place the lentils into a medium saucepan, cover with 2-3cm (1 inch) of water and add a big pinch is salt. Bring to the boil and cook until just tender, 20 to 25 minutes. Drain and refresh under cold water and drain again.
In a small frying pan (skillet), add the ginger and olive oil and heat over medium heat. Cook, stirring occasionally, until the ginger starts to turn golden and crispy, 8 to 10 minutes (or sooner, if the ginger darkens faster). Add the mustard seeds and chili and cook just until the seeds begin to pop, 30 to 45 seconds. Remove the pan from the heat.
In a large bowl, add the lentils, peaches, feta and then spoon over the oil, ginger and seeds. Season with salt and pepper and toss to combine. Top with basil and serve.