Combine beef, olive oil, and garlic in a large resealable plastic bag. Marinate in the refrigerator for at least 4 hours or overnight.
Preheat the grill to high. Grill on both sides for 3 to 4 minutes, for medium-rare. Let rest for 5 to 10 minutes and then slice thinly.
Puree the beans, garlic, olive oil, lemon juice, and thyme in a food processor until smooth. Season with salt and pepper, to taste.
Mix together the tomatoes, olive oil, vinegar, honey, and parsley, and season with salt and pepper, to taste. Heat grill to high. Flatten flatbread dough and gently press into a large rectangle and throw on grill. Grill on 1 side until golden, about 2 minutes. Remove from grill, turn over, and spread each flatbread with a thin layer of White Bean Puree, sliced beef, roasted shallots, and Tomato Chutney. Return to grill, close cover and cook for 2 minutes. Serve immediately.
Mix water and yeast in a large bowl and let stand 5 minutes to proof. Gradually pour in 2 cups of the flour and stir to incorporate. Mix for about 1 minute to form a sponge. Let stand, covered, for at least 1 hour.
Put sponge in the bowl of a stand mixer. Using the dough hook, add the salt and oil, then add the flour, 1/2 cup at a time, to form a dough. Remove from bowl and knead. Place in a clean oiled bowl and let rise, slowly, about 2 1/2 hours. Divide dough into 4 balls, if desired, let rise again for 1/2 hour, and then roll out as desired.
To roast shallots on the grill, place the shallot in the center of a piece of aluminum foil, drizzle with olive oil and season with salt and pepper. Bring the edges of foil together and scrunch to seal tightly. Place on a hot grill, close the cover and "roast" for 25 to 30 minutes or until soft. Remove the skin and slice.