For the Potatoes:

1. Place the potatoes in a large pot and cover with water. Add salt to the water. Set over medium-high heat and bring to a boil.
2. Meanwhile, preheat the oven to 450°F and line a large baking sheet with parchment paper. Brush the parchment with a little olive oil.
3. Cook the potatoes in the boiling water for about 10 minutes, or until they are easily pierced with a fork.
4. Drain the potatoes and then carefully transfer them to the baking sheet.
5. Using a small glass or jar, gently press down on each potato until it is flattened. Be gentle enough to ensure that the potatoes don’t break apart.
6. Drizzle the olive oil over the potatoes and season them with the salt and pepper.
7. Transfer the potatoes to the hot oven and bake for 25-30 minutes, or until the potatoes are deeply golden around the edges and crispy.

For the Stout Cheddar Sauce:

1. While the potatoes are baking, make the sauce by melting the butter in a saucepan over medium heat.
2. Once melted, add the flour to the butter and stir to combine. Cook for a minute or two.
3. Slowly whisk in the beer and the half-and-half.
4. Stirring frequently, bring the mixture to a gentle simmer and cook until thickened, about 5 minutes.
5. Stir in the cheese and cook until it is melted and the sauce is smooth.
6. Stir in the mustard. Season, to taste, with salt and pepper.

To Serve:

1. Transfer the cheese sauce to a bowl and place it on a platter. Arrange the potatoes on the platter around the cheese sauce.
2. Garnish with chopped fresh chives and serve while everything is hot.