Pick over the yellow split peas in a bowl and remove any hulls or stones. Rinse under cold water if needed and drain well.
Finely mince garlic to measure 2 tsp. Finely mince fresh ginger to measure 1 T. Zest lemons to measure 1 T and then squeeze enough lemon juice to measure 1/4 cup. Set these aside.
Heat 2 T extra-virgin olive oil in a small heavy Dutch oven over medium heat.
Add the 2 tsp minced garlic to the hot oil and sauté about 1 minute, until fragrant but not browned.
Add the 2 cups rinsed yellow split peas and stir several times to coat all the peas with oil.
Pour in 4 cups vegetable broth, increase heat just until the liquid comes to a low simmer, then reduce heat to maintain a low simmer. Cover and cook until the split peas are soft but not mushy and most of the liquid is absorbed, about 30–45 minutes, stirring occasionally to prevent sticking.
When the peas are soft and most liquid is absorbed, season to taste with salt and fresh‑ground black pepper. Stir in the 1 T lemon zest, 1 T minced ginger, and 1/4 cup lemon juice.
Replace the lid and let the split peas rest off the heat for 10–15 minutes to finish absorbing liquid and to develop the flavors.
While the peas are resting, chop cilantro and cut lemon wedges if using. Serve the split peas warm, sprinkled with chopped cilantro and with lemon wedges for squeezing, if desired.