In a medium skillet over medium heat, melt the butter and cook until the foam subsides. Place the apricots cut side down in the skillet and cook, stirring occasionally, until apricots are slightly tender and warmed through, 5 to 6 minutes. Meanwhile, in a small bowl, whisk together balsamic vinegar and the honey. When apricots are ready, and add honey-balsamic mixture to the skillet. Increase the heat to medium-high and cook, stirring frequently, until the apricots have cooked through and the glaze is bubbling, uniformly coating the apricots. To serve, place a scoop of ricotta on each serving plate, top with 2 apricot halves and drizzle with the honey-balsamic glaze from the skillet.