Peel and cut the potatoes into large even size chunks. Slice cabbage into 3-4 inch strips around 1/2-inch wide.
Place potatoes into a large pot and cover with 1-2 inches of cold water. Season with 1 teaspoon salt.
Bring potatoes to a boil over high heat, then lower to medium-high heat and continue to cook with a lid offset, for 10-12 minutes or until fork tender.
Meanwhile, melt 4 Tbsp butter in a large skillet over medium-high heat. Add the cabbage, green onions and fennel seeds to the melted butter. Sauté over medium-heat stirring occasionally while the potatoes cook, until tender.
To the cabbage add the half and half (or milk), remaining 1 teaspoon salt and black pepper, simmer gently on low for the flavors to blend, around 5-8 minutes.
Drain the potatoes well, and return to the pot, then mash.
To the mashed potatoes add the cabbage and onion mixture. Mix well until fully combined. Taste and adjust salt and pepper to your taste.
Serve immediately garnished with reserved green onion and pats of butter, if desired.