Make the dressing: Whisk the mustard, lemon juice, vinegar and a pinch of salt in a medium bowl. Slowly whisk in the olive oil and vegetable oil until smooth. Season with more salt.
Make the salad: Fill a large bowl halfway with ice water. Set a colander in the ice bath. Bring a medium pot of heavily salted water to a boil; add a pinch of sugar. Add the snap peas and cook 2 minutes. Remove with a strainer or slotted spoon and transfer to the colander in the ice bath to stop the cooking. Drain the snap peas and spread out on a kitchen towel; pat dry.
When ready to serve, transfer the snap peas to a large bowl and season with salt, the red pepper flakes and a pinch of sugar. Toss to blend. Add the raw snow peas and arugula and drizzle with the dressing; toss to coat. Serve immediately.
Photograph by David Malosh