Whisk apricot preserve in heavy medium saucepan over medium heat until melted and smooth, about 1 minute. Add mustard and whisk until beginning to simmer, about 30 seconds. Remove from heat. Stir in chopped rosemary. Season glaze to taste with salt and pepper.
(Can be made one day ahead. Cover & refrigerate. Stir over medium heat until heated through)
Heat oil in heavy large skillet over medium-high heat. Add sausages and sauté until browned and cooked through, about 10 minutes. Transfer to saucepan with glaze. Stir over medium heat until sausages are glazed, about 1 minute. Transfer to platter and serve.