Mix the mayonnaise, sour cream, chives and mustard in a bowl.
Bring a saucepan of water to a boil. Add the rice, 1/2 teaspoon salt and a few grinds of pepper; reduce the heat to low and simmer until almost tender, about 15 minutes. Add the asparagus and simmer until the rice and asparagus are tender, about 3 more minutes. Drain in a fine-mesh sieve and rinse under cold water, stirring gently to remove excess water. Transfer to a large bowl and stir in the lemon juice and half of the prepared chive sauce; season with salt and pepper.
Heat the butter in a large nonstick skillet over medium-high heat. Add the ham steaks, overlapping as necessary, and cook, flipping occasionally, until golden, about 5 minutes. Sprinkle the brown sugar over the ham and cook, flipping often, until the sugar melts. Season with pepper. Serve with the rice salad, the remaining chive sauce and lemon wedges.