In a medium saucepan over medium heat bring 1½ cups of water to a boil. Add the farro, and cook on medium-low heat until the farro is tender, about 20 minutes. Strain any remaining water then fluff the grains with a fork and set aside.
Heat a grill pan over medium heat until almost smoking. Add the slices of zucchini and summer squash, cooking until grill marks appear, about 2 minutes. Season with salt and pepper then flip the slices and cook an additional 2 minutes. Remove and set aside
Remove the small side muscle from the scallops and pat dry with a paper towel. Heat a large nonstick skillet over medium heat, add the olive oil and heat through. Season the scallops on both sides with salt and pepper then add the scallops to the pan.
Sear until the bottoms of the scallops are golden brown, about 3 minutes. Flip and add 2 tablespoons of the butter to the pan and cook for an additional 2 minutes.
Remove the scallops from the pan and set aside then add the remaining butter to the pan, cooking until the butter smells nutty and pale brown, about 3 minutes.
Add the lemon and chives to the pan, swirling to combine. Set the sauce aside until ready to serve.
Divide arugula among serving bowls and top with farro, corn, zucchini and squash. Top each with scallops and drizzle the pan sauce over the top. Garnish with the remaining chives and serve immediately.