Heat olive oil in a large Dutch oven or pot over medium heat.
Add bacon, and cook, stirring occasionally, until the bacon starts to look shiny and gets some color, about 5 minutes.
Add onion and cook, stirring occasionally, until golden and tender, about 5 minutes.
Add thyme sprigs, garlic, black-eyed peas, and 8 cups of cold water and bring to a simmer over medium-high.
Reduce heat to medium-low and simmer gently, skimming any foam from the surface, until beans are tender, 35–45 minutes.
Discard thyme; season with salt.
To serve, drizzle beans with oil and top with thyme leaves and cracked pepper.