Peel and chop potatoes into roughly equal-sized pieces about 1.5 inches across. Bring a large pot of salted water to a boil and add the potato pieces. Cook for 15 to 20 minutes until tender all the way through.

Lightly brush sausages with olive oil and season with salt and pepper on both sides. Heat a grill pan or skillet over medium-high heat and grill for 12 to 15 minutes total, turning every few minutes until they reach an internal temperature of 160 degrees Fahrenheit.

Drain cooked potatoes completely and return to the pot. Add butter and milk, then mash using a potato masher or fork until creamy and smooth. Taste and adjust seasoning with salt and pepper as needed.

In a bowl, combine sliced cucumber, chopped tomatoes, and thin red onion slices. Gently mix in sour cream or Greek yogurt and sprinkle with fresh parsley. Season with salt and pepper to taste.

Arrange creamy mashed potatoes on one side of each plate, place sausages next to them, and add a generous spoonful of garden salad on the other side. Garnish with extra fresh parsley if desired.