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1
Place the ham, bay leaves, and 3 quarts water in a large stock pot or dutch oven.
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2
Cover and bring to a boil over medium heat.
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3
Reduce the heat to low and simmer until meat is tender and pulls away from the bone, 2 to 2 1/2 hours.
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4
Remove the ham meat and bone from pot.
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5
When ham is cool enough to handle, shred the meat into bite sized pieces and set aside.
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6
Discard rind, fat, and bone.
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7
Add split peas and thyme to ham stock.
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8
Bring back to a boil, reduce the heat, and simmer, uncovered, until peas are tender but bot dissolved, about 45 minutes.
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9
While ham is simmering, heat oil in a large skillet over high heat until simmering.
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10
Add the onions, carrots, and celery and saute, stirring frequently, until most liquid evaporates and the vegetables begin to brown, 5 to 6 minutes.
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11
Reduce the heat to medium-low and add the butter, garlic, and sugar.
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12
Cook the vegetables, stirring frequently, until deeply browned, 30 to 35 minutes; set aside.
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13
Add the sauteed vegetables, potatoes, and shredded ham to the pot with the split peas.
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14
Simmer until the potatoes are tender and the peas dissolve ad thicken soup to the consistency of light cream, about 20 minutes more.
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15
Season with ground pepper to taste.
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16
(The soup can be refrigerated in an airtight container for 2 days.
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17
Warm the soup over low heat until hot.)
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18
Ladle the soup into bowls, sprinkle with red onion, if using, and serve, passing balsamic vinegar separately.
