In a large bowl, combine millet, shallot, garlic, carrot, zucchini, parsley, thyme, and olive oil and mix well. Add egg and mix until fully incorporated; season with salt and pepper.
Using a 1/2 cup dry measuring cup, scoop out millet mixture and lightly pack. Turn out onto work surface and flatten to make a burger. Repeat process making three more burgers.
Heat a large skillet over medium-high heat. Add canola oil. When the oil is heated, add burger, working in batches if necessary. Cook, gently turning once, until a golden crust has formed on the bottom, 8 to 10 minutes per side. Alternatively, the burgers may be baked in a 375-degree oven on a baking sheet for 30 minutes.
Serve on hamburger buns with lettuce and tomato and a dollop of yogurt.