Special equipment: one 12-cup mini muffin tin and one 24-cup mini muffin tin
Position two racks in the top and bottom thirds of the oven and preheat to 425 degrees F. Spray a 12-cup and a 24-cup mini muffin tin with cooking spray and set aside.
Cut the ham into small matchsticks similar in size to the hash browns. Set aside and reserve 1/3 cup of the ham. Mix the remaining ham, hash browns, 1 teaspoon salt and some pepper in a large bowl. Divide the mixture evenly among the sprayed cups, using about 1 rounded tablespoon each. Press the mixture in a thin layer across the bottom and up the sides of each cup to make a nest, leaving the edges uneven and jagged.
Bake, rotating the pans halfway through, until the nests are dark brown around the tips and golden and crisp on the outside, about 25 minutes.
Meanwhile, beat the cream cheese, lemon zest, milk 1/2 teaspoon salt, and some pepper together in a medium bowl with an electric mixer on medium-high speed. Scrape the mixture into a resealable plastic bag, cut off the tip and set aside.
When the nests are ready, remove them from the oven and let sit until they are cool enough to handle, about 10 minutes. Carefully lift the nests out of the tins using a small offset spatula or butter knife and transfer to a cookie sheet. Pipe the filling evenly among the nests. This may be done ahead; the nests can be set aside at room temperature until ready to serve, up to two hours.
When ready to serve, heat the filled nests until the cream cheese is warm and the potatoes are crisp, about 7 minutes. Meanwhile, bring a small pot of water to a boil. Add the frozen peas and cook until they are warm but not shriveled, 5 to 6 minutes. Drain the peas in a colander, shaking to remove excess water.
Transfer the nests to a serving platter. Top each with 1/4 teaspoon of the reserved ham, 3 peas and about 1/4 teaspoon chopped chives. Sprinkle with paprika and serve immediately.
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