Slice each tomato into medium-thick slices. Set aside.
Crack eggs into a shallow bowl. Scramble with a fork. Set aside.
Add flour to a second shallow bowl. Set aside.
Add Panko breadcrumbs to a third bowl. Set aside.
Dredge a tomato slice in flour. Turn to coat.
Remove from flour and place in egg. Turn to coat.
Remove from egg, allowing excess to drip off, and place in Panko breadcrumbs. Turn to coat.
Place slice on a paper towel or plate.
Repeat with remaining slices.
Place a cast iron skillet or sauté pan on medium-high heat, and add olive oil until entire bottom of the pan is covered.
When oil is hot and shimmering, add tomatoes to the skillet or sauté pan, a few at a time so they lie flat. Do not crowd. Tomatoes should not overlap.
Cook each tomato slice for approximately two minutes or until golden brown, then flip and cook on other side.
Once tomato slices are golden brown on both sides, remove from oil with a wire spatula and place on a paper towel-lined plate.
In a medium bowl, combine ranch dressing and Sriracha sauce. Set aside.
Serve tomato slices on a bed of hand-chopped romaine leaves.
Drizzle ranch mixture over tomatoes. Sprinkle with goat cheese crumbles.
Serve hot.