Slice the bread 1/2-inch thick; set aside 1/4 of the slices. Brush the remaining slices on both sides with olive oil and toast until golden brown on both sides in a broiler or on a grill. Set aside. (If bread slices are large, you may want to cut in half crosswise for easier serving.)
Tear the remaining bread slices into small pieces and whirl in a blender or food processor until you have fine bread crumbs. Pour 3 tablespoons olive oil into a wide frying pan and heat over medium-high heat. Add half of the minced garlic and stir for a few seconds until the garlic is fragrant. Add the bread crumbs to the pan with salt, to taste, and cook, stirring often, until toasted and crisp, 5 to 7 minutes. Set bread crumbs aside.
Wipe out the pan and in it, heat 2 more tablespoons of oil over medium-high heat. Add the remaining garlic. Cook, stirring for a few seconds, until the garlic is fragrant, then add the Swiss chard to the pan. Season the chard with salt to taste, stir a few seconds until wilted, then reduce heat, cover pan, and sweat chard until tender, about 10 minutes. If after cooking chard is very moist, squeeze out and discard excess water.
Meanwhile, drain the canned beans in a sieve set over a bowl. Measure out and reserve 1/2 cup of the bean liquid. Rinse the beans under cold water, then put in the blender or food processor with the zest and juice of the lemon, thyme, the reserved bean liquid, 1/4 cup olive oil, and salt to taste. Whirl until pureed, taste, and add more salt or lemon juice, if desired.
If made ahead, cover and refrigerate the bean puree and Swiss chard in separate containers; cover and store toasted bread slices and bread crumbs at room temperature. To serve, spread the bean puree thickly on bread slices, top with a spoonful of greens, then sprinkle with bread crumbs.