Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or aluminum foil.
Roll the pizza dough out on a lightly floured surface into a long, thin strip. The dough should be about 4-inches wide, 14-inches long, and less than 1/8-inch thick. Brush the surface of the dough with the oil. Sprinkle with the Parmesan, thyme, and red pepper flakes. Using a pizza cutter, slice the dough into 1/4-inch strips. Place on the prepared baking sheets. The strips can be laid straight or curved into designs. You can also twist 2 strips together. Leave 1/2-inch space between breadsticks.
Alternately, roll out the dough very thinly and pass through the fettucine cutter of a pasta machine.
Bake until browned and crispy, 10 to 15 minutes.
In a small bowl, dissolve the yeast and honey in 1/4 cup warm water.
In a food processor, combine the flour and the salt. Add the oil, the yeast mixture, and the remaining 3/4 cup of water and process until the mixture forms a ball. (The pizza dough can also be made in a mixer fitted with a dough hook. Mix on low speed until the mixture comes cleanly away from the sides of the bowl and starts to climb up the dough hook).
Turn the dough out onto a clean work surface and knead by hand 2 or 3 minutes longer. The dough should be smooth and firm. Cover the dough with a clean, damp towel and let it rise in a cool spot for about 2 hours. (When ready, the dough will stretch as it is lightly pulled).
Divide the dough into 4 balls, about 6 ounces each. Work each ball by pulling down the sides and tucking under the bottom of the ball. Repeat 4 or 5 times. Then on a smooth, unfloured surface, roll the ball under the palm of your hand until the top of the dough is smooth and firm, about 1 minute. Cover the dough with a damp towel and let rest 1 hour. At this point, the balls can be wrapped in plastic and refrigerated for up to 2 days.
In a small saucepan, combine the garlic cloves and olive oil and bring to a simmer. Reduce the heat and simmer until the garlic begins to turn brown, 10 to 15 minutes. (Do not let the garlic get too brown or the oil will have a bitter taste.)
Remove from the heat and cool to room temperature. Add the red pepper flakes and infuse for at least 2 hours to allow the flavors to blend. Refrigerate in a covered container for up to 2 weeks.