For banana ketchup: Preheat grill or grill pan on high. Brush each banana (with its peel still intact) with oil. Grill bananas on each side for about 5 minutes. Remove from grill and allow bananas to cool.
Peel bananas and break up into chunks and place into a blender. Add onion, garlic, tomato paste, dates, thyme, and water to the blender and blend until smooth, about 3 minutes.
Pour mixture into a large pot and stir in remaining ketchup ingredients. Bring mixture to a boil; lower the heat and simmer for 45 minutes to an hour. (If the mixture gets too thick, add water 2-3 tablespoons at a time).
Strain mixture through a fine sieve and store in an airtight container in the refrigerator until ready to use. (ketchup will hold for 5 to 6 months).
Preheat oven to 375°F.
Pour yucca fries into a large pot and fill with water. Place over medium- high heat and bring to a boil. Boil fries for about 15 minutes or until just fork tender.
Drain fries and spread onto a baking sheet. Drizzle with oil and season with salt and pepper. Toss together and redistribute fried into a single layer. Bake for 20 to 25 minutes or until fries are crisp on the outside and soft on the inside. Lightly season with salt and pepper and serve immediately with banana ketchup.