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1
For the buns: Stir the water, yeast and sugar together to activate the yeast.
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2
(You can tell when the yeast is activated-little bubbles will have formed, which will take a minute or two.)
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3
Add the melted butter and 3 of the eggs and mix until incorporated.
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4
Add 4 cups flour and the salt to the bowl of a stand mixer fitted with the dough hook attachment.
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5
Mix together on low speed, then stop and add the wet ingredients.
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6
Continue to mix until the dough is very smooth, about 5 minutes.
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7
You may want to add a little bit more flour as you mix; the dough should be sticky but workable.
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8
Transfer the dough to a bowl.
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9
Cover the bowl with a kitchen towel, place in warm area and let rise until the dough has doubled in size, about 30 minutes.
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10
After the dough has proofed (risen), turn it out onto a lightly-floured countertop and knead in the Cheddar and black pepper.
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11
Try not to overwork the dough; once the cheese is mixed in you can stop.
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12
Cut the dough into six equal portions and shape them into round balls.
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13
Place on a buttered baking sheet and flatten them with your hand.
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14
Cover and let rise again in a warm area until they have doubled in size, about 30 minutes more.
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15
When they are almost doubled in size, preheat the oven to 350 degrees F.
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16
Beat the remaining egg in a small bowl and brush the tops of the rolls with the egg.
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17
Bake until golden brown, rotating halfway through, 10 to 15 minutes.
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18
Cool on a wire rack.
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19
For the ketchup: Turn the oven down to 250 degrees F. Cut the garlic in half crosswise and sprinkle with olive oil, salt and pepper.
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20
Wrap in foil and roast until soft, 35 to 40 minutes.
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21
Remove the garlic from the skins and mix into a paste.
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22
Reserve 1 tablespoon for the ketchup, and use remaining garlic for another use.
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23
Whisk together the mayonnaise, mustard and roasted garlic in a bowl.
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24
Add the ketchup and vodka and mix until incorporated.
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25
This will keep for up to 6 days in the refrigerator.
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26
For cooking the burgers: Heat a skillet over high heat or heat an outdoor grill to high.
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27
Sprinkle the patties with salt and pepper.
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28
Coat with the oil and sear or grill until medium rare, 3 to 5 minutes per side.
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29
Slice the buns in half horizontally and brush with the melted butter.
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30
Toast in the skillet or on the grill.
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31
Arrange 8 pickle slices on each bottom bun and place a hamburger on top.
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32
Slather 1 to 2 tablespoons of spiked ketchup over the burger and set the top bun in place.
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33
Serve immediately with the remaining spiked ketchup on the side.
