Make the soup: If you have not yet, soak your split peas in water for 2 hours or overnight. This will improve the cook time of your soup. If the peas are not soaked, you will just need to cook them longer, about 30 to 40 extra minutes.
Heat the olive oil in a large pot over medium heat. Add the diced bacon and cook until crispy and brown. Use a slotted spoon to remove the bacon and rest it on a paper towel-lined plate. Pour off all but 1/4 cup of the drippings from the pot.
Place the pot back over medium heat and add the onions, garlic and marjoram leaves. Cook until they turn translucent, about 2 minutes.
Add the split peas, stock and milk and simmer until the peas start to fall apart, about 20 minutes.
Once cooked, transfer half of the peas and cooking liquid to a blender with half of the spinach. Puree until smooth, adding more liquid if needed to thin out the soup. Repeat this step for the remaining half of the peas and cooking liquid.
Combine all of the soup together and season with salt and lemon juice. Serve garnished with the bacon bits, sour cream and some fresh marjoram.
Make the grilled cheese: Using the flat side of a knife or the back of a spoon or fork, crush the cloves of garlic and place into a small microwave-safe bowl. Add the butter and microwave on high for about 30 seconds or until the butter is boiling hot and fully melted.
Brush the garlic butter over the back of the top and bottom pieces of bread for each sandwich. Flip the bread over and spread mayonnaise on each side and place 2 pieces of sharp white cheddar cheese in the middle of half of the pieces of bread.
In a saute pan or skillet over medium heat, toast the sandwich butter side down until an even brown color is achieved, about 1 1/2 minutes. Flip the sandwich and repeat on the other side.
Sprinkle with a pinch of salt, cut in half and serve hot with soup.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.