For queso fresco, heat milk in medium pot over medium-low heat, stirring frequently to prevent scorching, until milk reaches 165-180 degrees on instant-read thermometer. Slowly add lemon juice, constantly stirring. Allow to sit for about 20 minutes, so curds separate from whey.
Prepare colander with 4 layers of folded cheese cloth over large bowl. Using slotted spoon, transfer cheese curds to colander and allow to drain, about 1 hour.
Transfer cheese to a bowl and stir in salt to taste. Reserve.
For chimichurri, combine carrot tops, cilantro, parsley, jalapeño, garlic, and vinegar in food processor. Process until completely chopped. While processor is running, slowly pour in oil. Season to taste and reserve.
For carrots, bring medium pot of water to boil and season with salt to taste like the ocean. While water is heating up, prepare an ice water bath. Blanch carrots until tender, about 2 minutes. Place directly into ice water bath until chilled through. Remove and drain on paper towels.
In large cast-iron pan, heat oil over medium-high heat. Add carrots and cook until browned. Add butter and season to taste.
To serve, divide chimichurri among the bottom of 4 bowls or plates. Place roasted carrots on top and garnish with shaved radishes, queso fresco, and pea greens.