Interpreting beta coefficients in a regression model when fixing covariates Suppose I am interested in studying the effect of pizza on mortality across a number of countries.
y = Death [1/0]  
x1 = Pizza [1/0]  
x2 = Country [Italy/Germany/France]

In a logistic regression model, Country gets one-hot encoded so the model is:
y = b0 + b1 * Pizza + b2 * Italy + b3 * Germany + b4 * France
I'm interested to know how OddsRatio(b1) changes in Italy (vs. Germany and France). How should I proceed? Do I subset data to only Italy and rerun the LR model?
e.g. If I'm interested in Italy only, the model evaluates to y = b0 + b1 * Pizza + b2* Italy but this only provides the odds of death in Italy.

I'm a bit confused how mortality is a binary outcome... it sounds like you are leaving out some details about your data. That being said, it sounds like you're interested in whether the effect of pizza differs between countries. This is an interaction hypothesis, so something like: (note that if country is dummy coded then one level is left out - i.e. France is implicitly when Italy and Germany both =0).
y = b0 + b1 * Pizza + b2 * Italy + b3 * Germany + b4 * Pizza*Italy + b5 * Pizza*Germany

You would then evaluate the interaction effect by comparing the model fit of the model with the two interactions to the model fit of the model without the two interactions.
