In a 4 quart (or larger) dutch oven or stock pot, over medium-high heat, add oil or grease and ham. (If using ham hock, see step 4.)
Saute for 1 minute, add onion and continue to saute until ham and onions just begin to brown.
Reduce heat to low, add minced garlic and saute for 30 seconds.
Quickly add about 2 cups of water to the pot and increase heat to high. (If using ham hock, add now.)
Add dried beans, green beans and enough water to cover by at least 2 inches.
Bring to a boil, reduce heat to low/medium-low, cover and let simmer for 2 hours, checking every 1/2 hour to see if additional water is needed.
Add 2 teaspoons ham soup base, cover loosely (to allow some evaporation) and simmer 1 to 3 additional hours, occasionally checking liquid level in pot. (Allow liquid level to reduce to just barely covering the beans.)
Taste beans and add salt and pepper to taste.
NOTE: Small red potatoes may be added during last 1/2 hour of cooking if desired.