Cook and stir soppressata and garlic in a saucepan over medium heat until soppressata is crisp, about 5 minutes. Transfer soppressata to a plate, leaving garlic in the saucepan. Chop soppressata into small pieces.
Pour white wine into the saucepan and bring to a simmer, stirring to scrape up the browned bits from the bottom, about 5 minutes. Add butter; stir until melted, about 1 minute. Stir in spinach, artichoke hearts, and Parmesan cheese. Reduce heat to medium-low and cook, stirring occasionally, until mixture is heated through, 4 to 5 minutes. Stir in olive oil.
Mix soppressata, cream cheese, basil, parsley, onion powder, and black pepper together in a bowl.
Stir cream cheese mixture into the saucepan. Stir in milk until evenly blended and simmering, about 5 minutes. Remove from heat and let cool, stirring a few times to ensure bottom doesn't scorch, about 20 minutes. Transfer to a bowl and chill until serving.