Chop the artichoke hearts (easier to do while still partially frozen) and place in a bowl with 3 Tbsp olive oil, minced garlic, thyme, paprika, and pepper flakes (if using). Toss until artichokes are well coated. Dump out onto sheet pan, and move the mixture over to cover only 1/2 of the sheet pan, keeping the other half reserved for the asparagus.
Snap off the tough ends of the asparagus, and peel the remaining stalks if they are large and woody (small, tender ones don't need to be peeled). Snap them into 2" pieces (optional). Place the asparagus spears on the empty 1/2 of the baking sheet, toss them with a couple Tbsp of olive oil, and add salt and pepper to taste.
Warm a non-stick skillet over low heat (may want to add a little oil, eggs tend to stick to even non-stick skillets). Crack eggs into bowl, taking care not to break yolks (if you want to be extra cautious of getting perfect eggs, crack each egg into its own individual cup).
Place vegetable mixture into oven and start roasting. It will take about 10 minutes, but keep an eye on the vegetables so they do not burn, turning vegetables or shaking the pan occasionally.
After the vegetables have roasted for about 5-8 minutes, start the eggs. Slide the eggs into a warm skillet, sprinkle with salt and pepper and a pinch of paprika, and place cover over the skillet. Cook over low heat until the whites are firm but the yolks are still runny, about 4-5 minutes.
Serve: Squeeze fresh lemon juice over roasted artichokes, and place on plate as the bed. Arrange asparagus spears on the bed of artichokes and place baked eggs on top. Garnish with thyme.