Heat olive oil in a cast iron skillet over medium-high heat. Add potatoes and cook, stirring occasionally, until beginning to crisp, about 8β10 minutes.
Add onion and thyme, cook until softened and lightly caramelized, 5β6 minutes.
Push vegetables to the side, add sausage coins, and sear until browned on both sides. Toss everything together and season with salt and black pepper.
Make the Vinaigrette
In a mixing bowl, whisk together grainy mustard, Dijon mustard, vinegar, and honey.
Slowly stream in olive oil while whisking until emulsified. Season with salt and black pepper to taste.
Combine and Serve
Transfer hash to a platter or individual plates.
Drizzle with mustard seed vinaigrette and serve immediately.