Place the garlic cloves in a small saucepan and add enough olive oil to cover. Add the thyme and chili and cook over low heat until the garlic is very tender and lightly golden, about 40 minutes. Remove from the heat and let cool slightly.
Combine the beans, 10 cloves garlic confit, lemon or lime juice, salt, and pepper in a blender or food processor. Blend until smooth but still slightly textured, leaving a few tiny pieces of beans.
Taste and adjust the salt, pepper, and citrus. Transfer to a serving dish and spread into an even layer.
Drizzle with the garlic confit oil and scatter the red onion, parsley, and 3 to 4 cloves garlic confit over the top. Finish with coarse salt and freshly ground black pepper.
Serve immediately, or refrigerate in an airtight container for up to 3 days. Let the spread come to room temperature briefly before serving.