Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook until the vegetables start to soften.
Stir in the garlic and cook for one minute more. Add the split peas, chicken broth, ham, thyme, and bay leaf. Season with salt and pepper.
Bring the mixture to a boil, then reduce the heat and simmer uncovered for 45 minutes until the peas are tender and the stew thickens.
While the stew simmers, prepare the dumplings. In a mixing bowl, whisk together the flour, baking powder, and salt. Stir in the cheddar cheese.
Pour in the milk and melted butter and stir just until a soft dough forms. Do not overmix.
Drop spoonfuls of the dough onto the surface of the simmering stew. Cover the pot and cook for 15 minutes until the dumplings are cooked through and no longer doughy inside.
Remove the bay leaf before serving.