Combine 1/4 cup water and green onions in a blender; blend on the "Grate" setting.

Heat olive oil in 5-quart stockpot over medium heat. Pour in green onions. Cook and stir until fragrant, about 1 minute.

Combine 1/4 cup water and green tomatoes in a blender; blend on the "Grate" setting. Measure out 7 cups into the pot. Stir in chicken soup base, salt, pepper, and garlic. Pour in Chardonnay wine.

Heat remaining 1/2 cup water and cream in a saucepan over a medium heat, about 5 minutes. Add instant mashed potatoes; cook, stirring constantly, until potatoes have a loose consistency.

Stir potatoes into the stockpot. Cover soup and simmer, stirring frequently, until flavors combine, about 45 minutes.