Arroz Caldo (Filipino Chicken and Rice Soup)

Ingredients

• plus 3 tablespoons canola oil, divided
• freshly minced garlic , divided
• pounds boneless, skinless chicken thighs, cut into bite-sized pieces
• medium onion, thinly sliced
• tablespoon freshly minced ginger
• tablespoon Asian fish sauce
• teaspoon freshly ground black pepper, plus more to taste
• uncooked jasmine rice
• homemade chicken stock or low-sodium broth
• tablespoon calamansi, key lime, or lime juice
• Kosher salt
• scallions, thinly sliced
• hard-boiled eggs , cut into 1/4-inch slices
• fresh limes or calamansi, quartered