Core the tomatoes and cut into 1/2-inch-thick slices, then cut into 1-inch-thick strips making finger-shaped matchsticks. Season with salt and pepper.
Combine flour, thyme, and chipotle powder in a shallow dish and season with salt and pepper.
Crack eggs into a separate shallow dish. Add 2 tablespoons water and season with salt and pepper. Beat until smooth.
Place panko in a third shallow dish and season with salt and pepper.
Line a baking sheet with several layers of paper towel and set aside.
Heat oil in a large frying pan over medium heat. While oil is heating place a few tomato strips in the flour mixture, tossing to coat on all sides. Knock off any excess flour and place in the egg, turning to coat on all sides. Finally transfer the strips to the panko and press to coat the tomato on all sides.
The oil is hot enough if a cube of bread browns in 30 seconds. When the oil is ready, place a few tomato strips in the oil (don’t crowd the pan). Brown on one side (about 2-3 minutes) then flip and brown on the other side. Keep turning the strips until they are brown all over.
Remove tomato with tongs or a spatula, letting any excess oil drip back into the pan. Place on the prepared baking sheet and sprinkle with salt. Repeat with the remaining strips. If the tomato pieces start browning too quickly, lower the heat.
To make the burritos, warm the tortillas over medium heat in a dry cast iron skillet or nonstick frying pan until they are lightly toasted on both sides. Place 1/4 cup of rice and 1/4 cup of beans in the lower third of the tortilla. Top with a few tomato strips and fold the sides over, fold the bottom up over the sides then roll the tortilla away from you to close.
Toast the burrito seam-side-down, in the dry skillet to crisp the bottom, then flip and crisp the top, about a minute more. Serve immediately with salsa.