Preheat the oven to 350°F (175°C).
In a skillet over medium-high heat, melt 1/3 cup butter.
Add 1 Tbsp minced garlic and cook, stirring, until fragrant, about 30 seconds.
Add the drained and chopped artichoke hearts (1 14-oz can), 1 cup shredded Mozzarella cheese, 1 cup grated Parmesan cheese, and ½ cup sour cream to the skillet. Stir until evenly combined.
Season the mixture with salt and black pepper to taste. Remove the skillet from the heat and let the mixture cool for 1–2 minutes so it’s easier to handle.
Slice the 16-oz French bread loaf lengthwise into two halves.
Scoop out some of the soft center of each bread half to create a shallow cavity for the filling (discard or save the crumbs for another use).
Spoon the artichoke-cheese mixture evenly into both bread shells.
Sprinkle ½ cup shredded cheddar cheese evenly over the filled bread halves.
Place each filled half on a baking sheet and cover lightly with aluminum foil.
Bake covered for 25 minutes. Remove the foil and bake an additional 5–8 minutes, or until the cheese is fully melted and the top is lightly golden.
Let the bread rest for 2–3 minutes, then cut into slices and serve warm.