Wash the green bell pepper and pat dry. Slice, remove the seeds and white ribs, then dice. Peel and chop the garlic.
Add the diced bell pepper, chopped garlic, sugar, and white wine vinegar to a tall container. Using a hand blender, puree the mixture, then slowly add the olive oil while blending until well combined.
Tear the toast or bread roll into pieces, add to the blender, and continue blending until you reach your desired consistency. Season with salt and black pepper, then add cumin to taste, roughly 2 heaped teaspoons, until the sauce has the traditional mojo verde flavor.
Serve with papas arrugadas (wrinkled potatoes with a salt crust from the Canary Islands), as a sauce with grilled meat, or as a dip with bread.