Toss the chicken wings in a bowl along with a sprinkling of salt, half of the lemon juice and 1/4 cup olive oil. Transfer wings to a baking sheet and roast until the fat has begun to render and the skin starts to get crispy, 25 to 30 minutes.
Very carefully slice the carrots on a mandoline, then drop the slices into a bowl of ice water until ready to serve. Before serving, drain the carrots and add them to a serving dish. Drizzle with olive oil and season with salt.
Add the carrot juice, habanero, honey, white wine vinegar and the remaining lemon juice to a saucepan over medium-high heat. Bring to a boil and cook until reduced by half, 20 minutes. Finish the sauce with the butter, stirring until completely melted and fully integrated. Taste and adjust the seasoning as needed. Keep warm.
Add 4 inches of oil to a large Dutch oven and heat to 375 degrees F. Remove the chicken wings from the oven and, in batches, fry them in the oil until the skin is crispy, 4 to 5 minutes. Remove each batch of fried wings to a large bowl, add some of the reduced carrot sauce and toss to coat. Serve the wings on a platter, garnished with the blue cheese. Serve with the dressed carrots.