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1
In a large bowl gently combine the ground beef, salt, pepper, Worcestershire sauce and liquid smoke.
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2
Divide ground burger mixture into 4 equal segments and form them into thick patties.
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3
Refrigerate on a plate for 1 hour, then remove to and allow to come to room temperature, about 30 minutes before cooking.
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4
In a small bowl, mix together the garlic, mayonnaise and lemon juice and salt, to taste.
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5
Refrigerate until ready to serve.
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6
Warm a grill pan over high heat.
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7
Lightly brush the top of each burger with vegetable oil, then arrange on the grill, oiled side down.
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8
Sear until the burgers release easily from the grill and are brown, about 5 minutes.
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9
Brush with a bit more vegetable oil, flip and cook until the center slightly springs back, indicating a medium-rare center, another 5 minutes.
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10
While the burgers are finishing, brush both sides of the bread lightly with olive oil then put on the grill and cook until toasted, about 1 minute, then flip and toast the other side.
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11
Transfer 1 slice to each serving plate and spread with the garlic spread.
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12
Top each slice with a burger and while they are resting make the eggs to top each burger.
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13
In a small pan, melt 1 tablespoon of butter over low heat, crack an egg in the center, cover and cook until the white is set and the yolk is still runny, about 5 minutes.
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14
Slide the egg on top of the of the burger, season with a bit of salt and pepper, then finish with a few shakes of hot sauce.
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15
Repeat with the remaining butter and eggs and serve.
