Heat the oil in a small skillet over medium-high heat. Add the garlic and thyme and cook until the garlic is fragrant, about 45 seconds. Stir in the beans, water, and pepper (if the beans are unsalted, add a little salt, too). Turn the heat up to high and cook, stirring here and there and smashing the beans with your spatula, until the beans are saucy and the liquid is creamy, 2 to 4 minutes.
Using your spatula, make wells in the beans, one for each egg. Crack the eggs into the wells one at a time, then cover and cook until the whites are set but the yolks still jiggle when you shake the pan a bit, 1 to 2 minutes.
Taste, garnish with thyme leaves and season with a little more salt and pepper. Eat right away with toasted and oiled bread, if you want.