Put the potatoes in a large pot, cover with water by 2 inches and season generously with salt. Bring to a boil, then reduce the heat and simmer until the potatoes are tender when pierced with a knife, 12 to 15 minutes. Add the broccoli and cook until bright green and crisp-tender, about 1 more minute. Reserve 3 tablespoons cooking water, then drain the potatoes and broccoli.
Stir the cream cheese and reserved cooking water in a large bowl until smooth. Add the potatoes and broccoli and toss until evenly coated. Season with salt and pepper.
Toss the shrimp with the olive oil and everything seasoning in a medium bowl. Heat a large nonstick skillet over medium-high heat until very hot. Add the butter and let melt. Add the shrimp in a single layer and cook, turning halfway through, until browned, 3 to 4 minutes.
Stir the chives into the potato mixture. Divide the potato mixture and shrimp among plates. Sprinkle with more everything seasoning.