Preheat a grill to medium-high. Arrange the sausages on the grate and grill, turning, until cooked through, 15 to 20 minutes.
Meanwhile, in a small skillet, heat 2 tablespoons olive oil. Add the tomatoes and half of the chopped garlic; season with salt and pepper. Cook until thickened, about 3 minutes; remove from the heat.
In a bowl, mash half of the chickpeas with the remaining chopped garlic and 2 tablespoons olive oil; stir in the whole chickpeas and season with salt and pepper.
Brush the bread slices with the remaining 2 tablespoons olive oil and grill, turning once, until golden, about 1 minute; rub with the whole garlic clove. Working with 1 toast at a time, spread on the goat cheese, then top with the chickpea and tomato mixtures, drizzle with olive oil and sprinkle with the parsley. Serve with the sausages and cucumber spears.