1. **Prepare the Potatoes:**
– Grate the potatoes using a box grater or a food processor. Place the grated potatoes in a clean kitchen towel and squeeze out any excess moisture.
– Once the moisture is removed, transfer the grated potatoes to a bowl and season with salt and pepper.

2. **Make the Rösti:**
– Heat a large skillet (preferably non-stick) over medium-high heat and add the butter and olive oil.
– Once the butter is melted and the oil is hot, add the grated potatoes to the skillet. Press them down into an even layer, making sure they cover the bottom of the pan. Cook for 5-7 minutes until the bottom is golden brown and crispy.
– Flip the rösti over carefully using a spatula or by sliding it onto a plate and flipping it back into the pan. Cook for another 5-7 minutes on the other side, until crispy and golden.
– Remove the rösti from the pan and set it aside on a paper towel-lined plate to absorb any excess oil.

3. **Prepare the Toppings:**
– In a small bowl, mix the crème fraîche with a little lemon juice and a pinch of pepper. Stir until smooth.
– Arrange the smoked salmon on top of the crispy rösti. Top with a dollop of the crème fraîche mixture.
– Garnish with fresh dill, capers, and thinly sliced red onion.

4. **Serve and Enjoy:**
– Serve the rösti with a drizzle of lemon juice for an extra burst of freshness.
– Enjoy this crispy, savory dish as a perfect brunch or light dinner.