Cut off the dark green leaves of the leeks, leaving only the white and very light green section of each leek.

Rinse the leeks thoroughly to remove any sand or dirt.

Cut the unpeeled potatoes in half lengthwise. Slice 1/4 inch thick.

Melt 1 stick of butter over medium low heat in large stock pot.

Add leeks to butter. Cook leeks until soft, stirring often.

Add garlic to mixture. Cook 1 minute, stirring often.

Add chicken stock and potatoes to stock pot.

Bring to boil over medium heat, then reduce to simmer for 20 minutes, or until potatoes are fork tender.

Once potatoes are fork tender, remove from heat.

Stir in 1 cup of half and half, and stir in salt and pepper to taste.

Serve immediately, garnishing each serving with fresh cracked pepper and sliced green onions.