In a large skillet, heat olive oil over medium heat. Season the salmon fillets with salt and pepper, then place them skin-side down in the skillet. Cook for about 4-5 minutes, then flip and cook for another 3-4 minutes until cooked through. Remove the salmon from the skillet and set aside.

In the same skillet, add the butter and let it melt. Stir in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer.

Reduce the heat to low and stir in the heavy cream, Dijon mustard, dill, and lemon juice. Allow the sauce to simmer for about 5 minutes until slightly thickened. Season with salt and pepper to taste.

While the sauce simmers, prepare the dumplings. In a mixing bowl, combine the flour, baking powder, and salt. In another bowl, whisk together the milk and egg. Gradually add the wet ingredients to the dry ingredients, stirring until just combined.

Bring a large pot of salted water to a boil. Drop spoonfuls of the dumpling batter into the boiling water. Cook for about 10 minutes or until the dumplings float to the surface and are cooked through. Remove with a slotted spoon and set aside.

To serve, place a salmon fillet on each plate, spoon the creamy dill sauce over the top, and add a few dumplings on the side.