Heat oil in a large pot over medium heat. Add the bacon pieces and cook until golden and crisp. Remove some for garnish, if desired.
In the same pot with the bacon drippings, sauté the onion until translucent, then add the garlic and cook for about 1 minute until fragrant.
Sprinkle in the flour, stirring continuously to make a light roux. Cook for 1–2 minutes to remove the raw flour taste.
Slowly pour in the evaporated milk while stirring to avoid lumps. Then add water and the chicken cube. Stir until the cube is dissolved and the mixture begins to thicken slightly.
Add the broccoli and carrot. Cover and let simmer for 8–10 minutes, or until the vegetables are tender.
Stir in the shredded cheese until melted and the soup turns creamy. If you want it richer, add the all-purpose cream at this stage.
Season with salt and pepper to taste.
Serve hot, garnished with the reserved crispy bacon on top. Best enjoyed with crusty bread or toasted pandesal.