Make the vinaigrette: Blend the first 7 ingredients together in a food processor. With machine running, gradually add ¼ cup vegetable oil and process until well emulsified. Cover and let sit 30 minutes for the flavors to come together. May be prepared 1 day ahead kept refrigerated.
Heat olive oil in a medium saute pan over medium-high heat.
Add mushrooms, shallots, and minced garlic stirring often until the mushrooms release their liquid. Continue cooking stirring often until the pan becomes nearly dry again and the mushrooms begin to brown, about 6 more minutes. Deglaze the pan with vermouth.
Add a pinch of salt, pepper flakes, and arugula. Stir to slightly wilt.
Remove from heat. Stir in raw corn kernels. Set aside in a warm place.Sear the scallops: Season the scallops generously with salt and pepper.
Place a non stick or cast iron skillet over medium-high heat.
Add 1 tablespoon vegetable oil. Once the oil begins to shimmer add the scallops and sear for 2 ½ minutes, without moving them around. When the bottoms of the scallops look nicely browned and they release themselves from the pan turn them over and sear the other side for 1 to 1 ½ minutes. Using tongs, carefully transfer the scallops to a platter lined with paper towels to blot some of the oil.To serve: Toss the salad with a bit of vinaigrette.
Place some on each of 4 serving plates. Top with a scallop.