In a medium pot of boiling, salted water, parboil the potatoes for 5 minutes; drain.
In a large nonstick skillet, heat the oil over medium-high. Melt the butter in the oil, add the potatoes and cook until lightly brown, about 5 minutes. Add the apples and onion, season with salt, pepper and thyme, and cook, stirring occasionally, until the apples are crisp-tender and the potatoes are golden, 12 to 15 minutes. Remove from the heat. Top the hash with the cheese and cover the skillet with foil to melt.
Meanwhile, in a large, high-sided skillet, simmer the sausages in water to heat through. Butterfly the sausages (but do not halve), then, on a hot griddle or in a large skillet, cook until crisp on both sides.
Serve the wursts on the apple-potato hash and top with the mustard and honey.