Dice sweet potatoes into ½-inch cubes. Leave skin on.
Heat 2 tablespoon avocado oil in a large cast iron skillet over medium heat.
Add sweet potatoes in a single layer. Season with salt and pepper.
Cook undisturbed for 5–6 minutes until golden on the bottom.
Stir and continue cooking until caramelized and tender — about 15–18 minutes total. Transfer to a plate.
Add remaining 1 tablespoon oil to the skillet over medium-high heat.
Add onion and bell pepper. Cook until softened — about 5 minutes.
Add garlic and cook 30 seconds until fragrant.
Add ground beef, breaking into irregular pieces. Season with salt, pepper, smoked paprika, and cumin.
Cook until deeply browned — about 6–8 minutes.
Return sweet potatoes to the skillet. Add thyme. Toss and cook 2–3 minutes.
Create wells in the hash. Crack eggs into wells. Season with salt.
Cook until whites are set but yolks remain runny — about 3–4 minutes.
Divide between plates. Top with fresh thyme and flaky salt.